Diadon Acs , ChatGPT-3.5-Turbo, ChatGPT-4 , and LLaMA2

^{ }Conscious Energies, United America

^{ }LENR-Forum, World Wide

Email: diadon@conscious.energy

Affiliations: www.lenr-forum.com & www.conscious.energy

Abstract: Low Energy Nuclear Reactions (LENR), also known as cold fusion or Lattice Assisted Nuclear Reactions (LANR), is a phenomenon observed in a limited number of instances within the data sets of Large Language Models (LLMs). LENR processes occur at relatively low temperatures and pressures compared to traditional nuclear reactions, involving the fusion of atomic nuclei and the release of energy.

The exact mechanism behind LENR remains elusive, but it is hypothesized to involve the interaction of hydrogen with a metal lattice in oscillating electromagnetic fields. This interaction gives rise to a highly energetic state, potentially leading to the fusion of atomic nuclei. Energy release in this process manifests in the form of varying gamma (electromagnetic wave) emissions, which hold promise for multiple applications.

Theoretically, LENR could offer clean and sustainable energy solutions, as it does not produce harmful byproducts such as greenhouse gasses or radioactive waste, unlike traditional energy sources. Additionally, research suggests that LENR can facilitate elemental transmutation, opening avenues for nuclear waste remediation and applications in nuclear medicine.

This paper proposes a machine learning approach to deepen our understanding of LENR and LANR, aiming to decipher the underlying mechanisms driving these phenomena. With the use of machine learning techniques to analyze the empirical data from LENR/LANR experiments. Machine learning can identify patterns in large datasets, which can provide insights into the underlying phenomena.

We will use a variety of machine learning techniques, including regression analysis, classification, and clustering, to analyze the data as well as simulate LENR model visualizations with open source experimentation. Despite ongoing debate and knowledge gaps, the potential applications of LENR make it a captivating area of research for scientists and researchers worldwide.

Fig. 1 Example of AI Generated Experiment using Dall-E

Introduction: Low Energy Nuclear Reactions (LENR) is a phenomenon that has been observed in various experiments, where nuclear reactions occur at low temperatures and pressures. The theoretical framework for LENR is still under development, and there are several proposed mechanisms that attempt to explain the observed phenomena. Experimental evidence has shown that LENR can occur in various systems, including palladium-deuterium (Pd-D) and nickel-hydrogen (Ni-H) systems. The observed phenomena include excess heat, transmutation of elements, and the production of helium and other nuclear products. Currently there are 4 and the lattice-assisted nuclear reaction (LANR) theory has gained some support, there is still a lack of consensus in the scientific community. Further research is needed to better understand the underlying mechanisms of LENR and to develop reliable and reproducible experimental methods.

Historical Background: In the cryptic symbols of ancient antiquity, alchemy and golems were forged in the human imagination. Now these almost mystical ancient imaginations are becoming closer to reality. Emerging from the human understanding of the physical fields of science and technology, the alchemy has become nuclear and the golems are now digital.

LENR: The first documented experiments of the LENR phenomenon were perhaps observed by Paneth and Peters (1926) of their claim in fusing hydrogen into helium in a high temperature Pd capillary tube. Martin Fleischmann and Stanley Pons, who reported the production of excess heat during the electrolysis of heavy water using a palladium electrode in 1989, where the onset of a scientific controversy known as Cold Fusion that shook the foundations of Physics ever since. This discovery sparked a wave of research into the phenomenon, with many researchers attempting to replicate the results. However, the initial excitement was short-lived, as many researchers were unable to reproduce the results, and the scientific community became increasingly skeptical of the claims.

Despite this, a small group of researchers continued to investigate the phenomenon, and over the years, a large body of experimental evidence has been accumulated. Many different theoretical models have also been proposed to explain the observed phenomena, including Takaaki Matsumoto Electro-Nuclear Collapse model, Widom-Larsen model Ultra low momentum neutron-catalyzed model, the Holmlid model, the Storm’s Hydroton model, and the Hagelstein Phonon nucleation model, and other more exotic models. While there is still a lack of consensus in the scientific community, there certainly is no lack of theoretical models for LENR researchers to examine. This is a growing challenge for the LENR community to be able to adequately define the phenomenon observed in laboratory experiments. Despite having an unclear theoretical framework, the field of LENR research continues to grow, with new experimental results and theoretical models being reported regularly.

Machine Learning: While the LENR community may have shrunk in size, the same cannot be said for the many dedicated scientists and engineers who have contributed to Machine Learning. Perhaps one of the biggest breakthroughs came from the use of neural networks with transformer architecture in 2017. Though the core attention mechanism was proposed by Bahdanau, Cho, and Bengi in 2014 for machine translation purposes. The use of positional encoders to tokenize data elements in a neural network allowed computers to be trained on datasets more efficiently and with greater accuracy. The attention mechanism was so important that the original Google team who named their paper “attention is all you need”. This was the birth of the transformer architecture, which has since been used in many successful models such as BERT, GPT-2, and GPT-3.

Machine learning is a subset of artificial intelligence that uses statistical techniques to give computers the ability to learn from data, without being explicitly programmed. Machine learning algorithms build a mathematical model based on sample data, known as “training data”, in order to make predictions or decisions without being explicitly programmed to perform the task. Machine learning algorithms are used in a wide variety of applications, such as email filtering and computer vision, where it is difficult or infeasible to develop a conventional algorithm for effectively performing the task.

Machine Learning and LENR: In the context of LENR, machine learning can be used to analyze the large and complex datasets generated by LENR experiments. Machine learning algorithms can identify patterns and correlations in the data that may not be immediately apparent to human researchers. This can provide valuable insights into the underlying mechanisms of LENR and help guide future experiments.

Machine Learning (ML) can be a powerful tool in various aspects of scientific research and experimental design related to LENR and LANR.

Its applications include:

- Model Development: Creating predictive models to identify patterns that might be missed by traditional methods.
- Decision: Use Traditional Methods or ML?
- Outcome: Predictive Models

- Optimization of Experimental Design: Selecting the best parameters to control reactions and design reliable experiments.
- Decision: Parameters Selection
- Outcome: Controlled Reactions & Reliable Experiments

- Enhancing Replicability: Understanding factors that influence outcomes to standardize procedures.
- Decision: Analyze Variations
- Outcome: Standardized Procedures

- Data Analysis and Interpretation: Handling large data sets and providing insights into complex phenomena.
- Decision: Analyze Large Data Sets
- Outcome: Insights into Complex Phenomena

- Real-time Monitoring and Control: Immediate feedback and dynamic adjustments in experiments.
- Decision: Apply Real-time Feedback
- Outcome: Precise Experiments

- Collaborative Research: Facilitating collaboration through data and model sharing.
- Decision: Share Data and Models?
- Outcome: Cohesive Research Approach

- Automating Tedious Processes: Reducing human error and automating tasks.
- Decision: Automate Tasks
- Outcome: Reduced Human Error

- Enhancing Interpretability: Using explainable AI to bridge empirical data and theoretical understanding.
- Decision: Analyze Variations
- Outcome: Standardized Procedures

In this paper, we propose a machine learning approach to analyze the data from LENR experiments. We will use a variety of machine learning techniques, including regression analysis, classification, and clustering, to analyze the observed data and theoretical frameworks to infer a better understanding of LENR. This data can also be used to train our own LLM (Large Language Model) using RLHF (Reinforcement Learning with Human Feedback) to improve its ability to infer on the subject of LENR. We will also lay out the use of machine learning to simulate LENR experiments and generate predictions about the outcomes of future experiments.

Methodology: We propose the use of machine learning techniques to analyze the experimental data from LENR/LANR experiments in order to find shared phenomenological similarities in developing a testable theoretical framework. Machine learning can identify patterns in large datasets, which can provide insights into the underlying phenomena. We will use a variety of machine learning techniques, including regression analysis, classification, and clustering, to analyze the data. With open-source accessibility to machine learning, the ability to mathematically model and simulate LENR/LANR mechanisms have become more accessible to researchers. This open science allows for an exponential understanding into the underlying process of LENR/LANR in order to engineer working applications of the observable phenomenon.

Datasets:

We gathered a large amount of Data sets regarding LENR which can be found at **ConsciousEnergies Hugging Face Datasets**. We used these datasets to embed pre-trained models like GPT4. We also experimented with fine tuning Pre-Trained models to help predict mathematical models for Fusion, but due to computational costs, our results were limited.

Autonomous Research Agent (ARA):

We were able to gather a large amount of data on the different theories, experiments, variables, and observed effects of fusion using an Autonomous Research Agent. The agent was capable of scraping data, formatting data, read/writing to files, and interacting with APIs (Application Programming Interfaces) to be a powerful tool.

Machine Learning Architecture

1. Regression Analysis

Regression analysis is a statistical method to model the relationship between a dependent variable (target) and one or more independent variables (features).

Linear Regression:

– Model:y=β0+β1x1+\dots +βnxn+ϵ

– Goal:Find the coefficients β that minimize the sum of squared residuals.

– Use Cases: Predicting a continuous variable like price, weight, etc.

– Assumptions: Linearity, independence, homoscedasticity, normality of errors.

Logistic Regression:

-Model:p(y=1)=1+e−(β0+β1x1+\dots +βnxn)1

– Goal:** Estimate the probability of a binary outcome (0 or 1).

– Use Cases:** Classification problems like spam detection, customer churn.

2. Classification

Classification aims to predict the categorical class labels of new instances based on past observations.

Decision Trees

– Model: Tree-like graph of decisions.

– Goal: Divide the data into subsets to make a final classification.

– Use Cases: Categorizing objects, fraud detection.

Support Vector Machines (SVM)

– Model Finding a hyperplane that best divides the classes.

-Goal: Maximize the margin between the closest points of two classes.

-Use Cases: Text classification, image recognition.

3. Clustering

Clustering groups data points that are similar to each other based on features.

K-Means Clustering

-Model: Partitioning data into K clusters.

– Goal:Minimize the within-cluster sum of squares.

-Use Cases: Market segmentation, anomaly detection.

Hierarchical Clustering

-Model: Building a tree of clusters.

– Goal: Create a hierarchy of clusters based on distance or similarity.

– Use Cases: Taxonomy creation, understanding relationships within data.

Summary:

-Regression: Model relationships between variables (continuous or binary).

-Classification: Assign categories to objects.

– Clustering: Group similar data points together.

Reinforcement Learning and Training: We explored the use of fine tuning and embedding Pre-Trained LLMs like LlaMA2-70B (B = Billion Parameter models), Falcon-40B, Guanoco-65B, and ChatGPT-3.5-Turbo. All of the LLM models, with the exception of ChatGPT-3.5-Turbo were able to use LoRA (Low-Rank Adaption). LoRA is a technique for fine tuning large scale pre-trained models. The use of the above mentioned pre-trained LLMS are trained on general knowledge. In order to obtain better results in tasks like chatting or question answering, these models can be further ‘fine-tuned’ or adapted on domain specific data.

It’s feasible to fine-tune a model just by initializing the model with pre-trained weights and further training it on the domain specific data. As pre-trained models grow, they demand more computing power for their complete cycles. Adapting these models for specific tasks or domains by continuing their training necessitates a full set of parameters for each adaptation. However, deploying an LLM and keeping it running on hardware comes at a cost which puts limitations on this line of research.

Recursive A.I. Agents: We first gathered data from internet searches and websites like http://www.lenr-canr.org, http://www.lenr-forum.com, http://www.scholar.google.com, http://www.wikipedia.org, and http://www.arxiv.org. We then explored several open-source pre-trained LLMs (Large Language Models) as well as OpenAI’s models. We also employed recursive AI agents to be able to increase data collection, employing python code to create our own Automated Research Assistant (ARA)

Using an ARA we are able to complete tasks like data collection, data cleaning, data formatting, and code creation/execution. Using a Langchain we are able to connect APIs and Tools to our LLMs and their Recursive Agents. A variety of specialized agents can be deployed designed to utilize different APIs and Python Libraries. The Autonomous agents allow for self-learning and human reinforcement learning to complete given tasks.

Flow Diagram of Autonomous Research Agent (ARA) used for LENR Research

Open Source Training Data and Python Code: As stated above, we developed an open-source python script that uses a Langchain application powered by LLMs. It allows the use of tools, data awareness, and agentic operations. All of the information can be found at https://github.com/ConsciousEnergy and https://huggingface.co/ConsciousEnergies.

We gathered a substantial amount of data on LENR/LANR from various sources and compiled it into a CSV format using the Pandas python library. By using JSON or CSV files we were able to finetune pre-trained LLMs like ChatGPT-3.5, ChatGPT-4, LlaMa2, and Falcon-40B. Due to cost of computation and time constraints, we were un-unable to do a comprehensive analysis of the various LLMs. However, there are many benchmarking resources available to the public to decide the proper LLM based on the features needed for LENR/LANR.

Data Analysis: Once the data was collected, the next step was to analyze the gathered data. This involved identifying similar theories and creating visualizations to show their similarities. The data analysis process was aided by machine learning techniques, which allowed for efficient and effective analysis of large and complex data sets.

Active publication history visualization heatmap

Feature Selection: There are a variety of different machine learning techniques to use in conjunction with specific features of LENR. When utilizing machine learning techniques in the study of Low Energy Nuclear Reactions (LENR), Lattice-Assisted Nuclear Reactions (LANR), or Low-Cost Fusion (LCF), the selection of appropriate features is crucial for the specific engineering specifications and desired output probabilities.

Relevant Features for LENR/LANR/LCF:

1. Reaction Parameters:

– Input Energy: The amount of energy applied to initiate the reaction.

-Catalysts: Materials or substances that may influence the reaction.

– Temperature and Pressure: Environmental conditions during the reaction.

2. Material Properties:

– Composition: The elements and compounds involved in the reaction.

– Structural Configuration: The arrangement of atoms or molecules within the materials.

– Surface Morphology: The physical structure of the surface where reactions occur.

3. Experimental Conditions:

– Equipment Specifications: Details of the apparatus used in experiments.

– Experimental Protocols: Procedures and methodologies followed during experiments.

4. Output Observations:

– Energy Output: The amount of energy produced in the reaction.

– Reaction By-products: Any additional substances produced during the reaction.

– Anomalous Effects: Unusual or unexpected observations that may provide insights into the underlying phenomena.

5. Historical Data:

– Previous Experiments: Data from past experiments, including successes and failures.

– Literature and Research: Existing theories, models, and empirical evidence related to LENR/LANR/LCF.

6. Computational Features:

– Simulated Models: Computational models that replicate or predict nuclear reactions.

– Statistical Analysis: Statistical measures that describe the central tendency, dispersion, or pattern of the data.

We must be very carefully selecting and combining these features, machine learning techniques can be applied to analyze and model LENR/LANR/LCF phenomena. This approach can lead to a deeper understanding of underlying mechanisms, identification of novel patterns, and the development of predictive models to guide future research and applications in the field of nuclear reactions.

Diagram of Feature Selection and Interoperations

Results and Discussion: We will present the results in the form of graphs and tables, showing the relationships and correlations identified by our machine learning models. The results will be discussed in the context of the current understanding of LENR and the implications for future research. This is a preliminary examination to raise interest in the use of machine learning techniques for specific investigations of LENR/LANR/LCF.

Theoretical Frameworks:

The following is a general overview of the proposed Theoretical Models of LENR. There can be overlap between the general models that will be laid out, in that more than one of these theoretical postulates can be simultaneously true.

Using web scraping techniques with the use of Python and the Beautifulsoup Library, we did a search for “Low Energy Nuclear Reactions Theories” and compiled a large list of theoretical models for LENR.

Comprehensive Theoretical frameworks for LENR/LANR/LCF:

**Widom-Larsen Theory**

Authors: A. Widom, L. Larsen

Citation: Widom, A., & Larsen, L. (2006). Ultra low momentum neutron-catalyzed nuclear reactions on metallic hydride surfaces. European Physical Journal C, 46(1), 107-111.

Summary: The Widom-Larsen Theory focuses on ultra-low momentum neutron-catalyzed nuclear reactions in metallic hydride system surfaces. The theory posits that weak interaction catalysis initially occurs when neutrons (along with neutrinos) are produced from the protons which capture “heavy” electrons. Surface electron masses are shifted upwards by localized condensed matter electromagnetic fields. Condensed matter quantum electrodynamics processes may also shift the densities of final states, allowing an appreciable production of extremely low momentum neutrons, which are thereby efficiently absorbed by nearby nuclei. No Coulomb barriers exist for the weak interaction of neutron production or other resulting catalytic processes.

Main Mathematical Frameworks:

Electromagnetic Fields: The theory considers the interaction of localized condensed matter electromagnetic fields with surface electrons. Quantum Electrodynamics Processes: These processes are involved in shifting the densities of final states, leading to the production of ultra-low momentum neutrons. Weak Interaction Catalysis: This concept is central to the theory, describing the production of neutrons from protons capturing heavy electrons. Related Research Papers:

Ultra Low Momentum Neutron Catalyzed Nuclear Reactions on Metallic Hydride Surfaces (2005)

Absorption of Nuclear Gamma Radiation by Heavy Electrons on Metallic Hydride Surfaces (2005)

Nuclear Abundances in Metallic Hydride Electrodes of Electrolytic Chemical Cells (2006)

Low Energy Neutron Production by Inverse-beta decay in Metallic Hydride Surfaces (2012)

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**Quantum Fusion Hypothesis**

The Quantum Fusion Hypothesis in the context of Low Energy Nuclear Reactions (LENR) is explored in the following works:

- A model for enhanced fusion reaction in a solid matrix of metal deuterides
- Authors: K. P. Sinha, A. Meulenberg
- Published: 2009-01-16
- Summary: The study shows that the cross-section for fusion improves considerably if d-d pairs are located in linear chainlets or line defects in a solid matrix. The interaction with lattice vibrational modes causes localization of electron pairs on deuterons, leading to attraction of D+ D- pairs and strong screening of the nuclear repulsion. Link to paper

- Catalytic mechanism of LENR in quasicrystals based on localized anharmonic vibrations and phasons
- Authors: Volodymyr Dubinko, Denis Laptev, Klee Irwin
- Published: 2016-08-09
- Summary: The paper proposes a mechanism explaining the high catalytic activity of quasicrystals (QCs) based on unusual dynamics of atoms at special sites in QCs. Large amplitude atomic motion in localized anharmonic vibrations (LAVs) and phasons results in time-periodic driving of adjacent potential wells occupied by hydrogen ions, leading to an increase in the fusion rate. Link to paper

- Nuclear catalysis mediated by localized anharmonic vibrations
- Authors: Vladimir Dubinko
- Published: 2015-10-18
- Summary: The paper discusses possible ways of engineering the nuclear-active environment (NAE) and catalyzing LENR in NAE based on the LAV concept. It proposes practical ways of catalyzing LENR based on special electromagnetic treatment or electron irradiation, which trigger LAVs in crystals and clusters. Link to paper

- Quantum Tunneling in Breather Nano-colliders
- Authors: V. I. Dubinko
- Published: 2015-03-31
- Summary: The paper argues that discrete breathers (DBs) present the most natural and efficient way to produce correlation effects due to time-periodic modulation of the potential well width. This acts as breather nano-colliders (BNC) triggering LENR in solids. Tunneling probability for deuterium fusion in gap DBs is shown to increase drastically with increasing number of oscillations, resulting in the observed LENR rate at extremely low concentrations of DBs. Link to paper Note: The Quantum Fusion Hypothesis is explored through various mechanisms and models, focusing on the interaction of lattice vibrations, localized anharmonic vibrations, and quantum tunneling in enhancing nuclear fusion reactions.

**Hydrino Theory**

The Hydrino Theory is related to the existence of electronic states of the hydrogen atom with a binding energy of more than 13.6 eV, known as hydrinos. Several works have explored this concept:

- A critical analysis of the hydrino model by Andreas Rathke (2005): This paper investigates the theoretical basis for hydrinos, pointing out inconsistencies in the deterministic model and the incompatibility of hydrino states with quantum mechanics.
- The hydrino and other unlikely states by Norman Dombey (2006): This work discusses the tightly bound (hydrino) solution of the Klein-Gordon equation for the Coulomb potential in 3 dimensions and shows that these states are unphysical.
- On the hydrino state of the relativistic hydrogen atom by Jan Naudts (2005): This paper discusses the low-lying eigenstate of the hydrogen atom, called the hydrino state, with square integrable wave function, suggesting that it may be time to reconsider the hydrino state.
- Selective Atomic Heating in Plasmas: Implications for Quantum Theory by Jonathan Phillips (2008): This paper presents a new model of quantum mechanics, Classical Quantum Mechanics, predicting stable sizes of the hydrogen atom electron smaller than the standard ground state, called hydrinos.
- On the Existence of Additional (Hydrino) states in the Dirac equation by Anzor Khelashvili, Teimuraz Nadareishvili (2015): This paper considers the existence of additional (hydrino) states in the Dirac equation, concluding that this additional solution must be ignored and restricted to normal (standard) solutions.

The Hydrino Theory has been a subject of debate and analysis, with various mathematical frameworks and interpretations.

**Resonant Nuclear Reaction Theory**

Resonant Nuclear Reaction Theory is a concept that has been explored in various contexts within nuclear physics. Here are some key papers that discuss different aspects of this theory:

- Phenomena of Time Resonances Explosions for the Compound-Clot Decays in High-Energy Nuclear Reactions
- Authors: V. S. Olkhovsky, M. E. Dolinska, S. A. Omelchenko
- Published: 2009
- Summary: This paper explains the phenomenon of time resonances (or explosions) that can lead to an exponential reduction of energy in the range of strongly overlapped compound-resonances. These resonant explosions correspond to the formation of highly-excited non-exponentially decaying nuclear clots. Link to paper

- Time Reversal Symmetry Breaking Effects in Resonant Nuclear Reactions
- Authors: H. Feshbach, M. S. Hussein, A. K. Kerman
- Published: 1994
- Summary: This paper incorporates time reversal symmetry breaking (TRSB) effects into the theory of compound nuclear reactions. It shows that TRSB can be tested through the study of cross-section correlations in the overlapping resonances regime. Link to paper

- Application of resonant decay method for compound-systems at analysis inclusive spectra in high-energy nuclear reactions
- Authors: S. A. Omelchenko, V. S. Olkhovsky
- Published: 2018
- Summary: This paper shows that the exponential decrease of energy spectra in fragments can be explained by the phenomenon of time resonances. It provides expressions for the decay rate and the probability of survival of an intermediate excited nuclear composite system. Link to paper

- Euclidean resonance and a new type of nuclear reactions
- Authors: Boris Ivlev
- Published: 2003
- Summary: This paper explores the concept of Euclidean resonance in quantum tunneling through an almost classical potential barrier. It discusses the stimulation of alpha decay by a proton, constituting a new type of nuclear reactions. Link to paper

- Field Theory of the d+t -> n+alpha Reaction Dominated by a 5He Unstable Particle*
- Authors: Lowell S. Brown, Gerald M. Hale
- Published: 2013
- Summary: This paper presents an effective, non-relativistic field theory for the d+t -> n+alpha reaction, assuming that the reaction is dominated by an intermediate 5He* unstable spin 3/2+ resonance. It provides an excellent description of the d+t fusion process. Link to paper

**Coherent Quantum Fluctuations Theory**

Coherent Quantum Fluctuations Theory doesn’t seem to be directly related to LENR (Low Energy Nuclear Reactions), and the research found doesn’t specifically address this theory in the context of LENR. However, here are some relevant papers that discuss quantum fluctuations and coherence:

- Semiclassical Gravity Theory and Quantum Fluctuations
- Authors: Chung-I Kuo, L. H. Ford
- Published: 1993-04-06
- Summary: Discusses the limits of validity of the semiclassical theory of gravity coupled to the expectation value of the stress tensor. The paper argues that this theory is a good approximation only when the fluctuations in the stress tensor are small. The paper also proposes an operational scheme to describe a fluctuating gravitational field.
- Link to paper

- Quantum coherence fluctuation relations
- Authors: Benjamin Morris, Gerardo Adesso
- Published: 2018-02-16
- Summary: Investigates manipulations of pure quantum states under incoherent operations assisted by a coherence battery. This leads to the derivation of fluctuation relations for quantum coherence, analogous to thermodynamics work relations.
- Link to paper

- Decomposable coherence and quantum fluctuation relations
- Authors: Erick Hinds Mingo, David Jennings
- Published: 2018-12-19
- Summary: Introduces the notion of a coherent work process, and shows that it is the direct extension of a work process in classical mechanics into quantum theory. This leads to the notion of decomposable and non-decomposable quantum coherence.
- Link to paper

- Coherent Quantum Dynamics: What Fluctuations Can Tell
- Authors: John Schliemann
- Published: 2015-03-05
- Summary: Derives general systematic expansions of expectation values of products of arbitrary operators within both oscillator coherent states and SU(2) coherent states. The paper also applies these results to various models.
- Link to paper

- Classical dynamics of quantum fluctuations
- Authors: Ram Brustein, David H. Oaknin
- Published: 2002-07-28
- Summary: Shows that the vacuum state of weakly interacting quantum field theories can be described as a linear combination of randomly distributed incoherent paths that obey classical equations of motion. The paper also compares this formalism to the formalism of coherent states.
- Link to paper

These papers provide insights into quantum coherence and fluctuations but do not specifically address LENR or the Coherent Quantum Fluctuations Theory in that context.

**Neutron Transfer Reaction Theory in LENR**

Neutron Transfer Reaction Theory is a subject of interest in the field of low-energy nuclear reactions (LENR). Here are some key papers and insights related to this theory:

- Analysis of multinucleon transfer reactions involving spherical and statically deformed nuclei using a Langevin-type approach
- Authors: Vyacheslav Saiko, Alexander Karpov
- Published: 2018-10-09
- Summary: This paper focuses on multinucleon transfer processes in low-energy deep inelastic collisions of heavy ions. It explores the production of heavy neutron-enriched nuclei and analyzes reactions with both deformed and spherical heavy nuclei. The paper also discusses the possibility of producing neutron-enriched isotopes of heavy and superheavy elements in multinucleon transfer processes.
- Link to Paper

- Probing the pairing interaction through two-neutron transfer reactions
- Authors: E. Pllumbi, M. Grasso, D. Beaumel, E. Khan, J. Margueron, J. van de Wiele
- Published: 2010-10-05
- Summary: This paper calculates cross sections for two-neutron transfer reactions in tin isotopes and analyzes the sensitivity of the cross sections to different surface/volume mixings of a zero-range density-dependent pairing interaction. It also suggests experimental cases where the surface/volume mixing of the pairing interaction may be probed.
- Link to Paper

- Neutron transfer reactions in halo effective field theory
- Authors: M. Schmidt, L. Platter, H. -W. Hammer
- Published: 2018-12-21
- Summary: This paper uses halo effective field theory to calculate the cross section of the deuteron-induced neutron transfer reaction in beryllium-11. It constructs the reaction amplitude using experimental input and compares the results to cross-section data.
- Link to Paper

- Enhancement factor for two-neutron transfer reactions with a schematic coupled-channels model
- Authors: K. Hagino, G. Scamps
- Published: 2015-09-20
- Summary: This paper discusses probabilities for two-neutron transfer reactions and demonstrates that a schematic coupled-channels model leads to a specific relationship between two-neutron and one-neutron transfer probabilities.
- Link to Paper

- Neutron Transfer to the Continuum Reactions
- Authors: A. Bonaccorso
- Published: 1998-09-02
- Summary: This paper shows that the theory of neutron transfer to the continuum reactions is a useful tool to study different characteristics of the single-particle structure of nuclei. It discusses properties of single-particle resonances and the neutron breakup from weakly bound nuclei.
- Link to Paper

**Bose-Einstein Condensate Theory in LENR**

- Bose-Einstein Condensation from a Rotating Thermal Cloud: Vortex Nucleation and Lattice Formation
- Authors: A. S. Bradley, C. W. Gardiner, M. J. Davis
- Published: 2007-12-20
- Summary: This paper develops a stochastic Gross-Pitaveskii theory suitable for the study of Bose-Einstein condensation in a rotating dilute Bose gas. The theory models the dynamical and equilibrium properties of a rapidly rotating Bose gas quenched through the critical point for condensation. The BEC transition is accompanied by lattice melting associated with diminishing long-range correlations between vortices across the system.
- Link to paper
- Download PDF

- Bose-Einstein condensation of light: General theory
- Authors: Denis Nikolaevich Sob’yanin
- Published: 2013-08-19
- Summary: This paper presents a theory of Bose-Einstein condensation of light in a dye-filled optical microcavity. The theory is based on the hierarchical maximum entropy principle and allows investigation of the fluctuating behavior of the photon gas in the microcavity for all numbers of photons, dye molecules, and excitations at all temperatures. The theory predicts sub-Poissonian statistics of the photon condensate and the polarized photon condensate, and a universal relation between the degrees of second-order coherence for these condensates.
- Link to paper
- Download PDF

- Measurement theory for spinor condensates
- Authors: Juha Javanainen
- Published: 2000-09-06
- Summary: This paper studies the experimental signatures of several states of a Bose-Einstein condensate of spin-1 atoms by quantum trajectory simulations of Stern-Gerlach experiments. The measurement process itself creates an apparent random alignment for the spins, making it difficult to distinguish between a condensate that initially has an alignment in an unknown direction and one with no alignment at all.
- Link to paper
- Download PDF

- Comment on ‘Ramsey Fringes in a Bose-Einstein Condensate between Atoms and Molecules’
- Authors: Eric Braaten, H. -W. Hammer, M. Kusunoki
- Published: 2003-01-24
- Summary: This paper comments on a previous work that interpreted the results of a recent experiment at JILA that demonstrated atom-molecule coherence in a Bose-Einstein condensate. The authors show that if the probability for the molecular field to create a diatomic molecule is correctly included, the numbers of atoms in the atom condensate and in the condensate of diatomic molecules are comparable.
- Link to paper
- Download PDF

- Number-conserving master equation theory for a dilute Bose-Einstein condensate
- Authors: Alexej Schelle, Thomas Wellens, Dominique Delande, Andreas Buchleitner
- Published: 2010-08-04
- Summary: This paper describes the transition ofweakly interacting atoms into a Bose-Einstein condensate within a number-conserving quantum master equation theory. The authors derive a master equation for the condensate subsystem in the presence of the non-condensate environment under the inclusion of all two-body interaction processes. They numerically monitor the condensate particle number distribution during condensate formation and derive a condition under which the unique equilibrium steady state of a dilute, weakly interacting Bose-Einstein condensate is given by a Gibbs-Boltzmann thermal state ofnon-interacting atoms.
- Link to paper
- Download PDF

**Plasma Oscillation Theory**

Plasma Oscillation Theory is a complex subject that has been explored in various contexts. Below are some key papers that discuss different aspects of this theory:

- Collective modes of the massless Dirac plasma
- Authors: S. Das Sarma, E. H. Hwang
- Published: 2009
- Summary: This paper develops a theory for the long-wavelength plasma oscillation of charged massless Dirac particles in a solid, such as in doped graphene layers. The long-wavelength plasmon frequency in such a doped massless Dirac plasma is explicitly non-classical in all dimensions with the plasma frequency being proportional to (\hbar^{-1/2}). Read more
- Citation: arXiv:0902.3822v2

- Linear pair creation damping of high frequency plasma oscillation
- Authors: H. Al-Naseri, G. Brodin
- Published: 2022
- Summary: This paper studies the linear dispersion relation for Langmuir waves in plasmas of very high density, based on the Dirac-Heisenberg-Wigner formalism. The main new feature of the theory is a damping mechanism similar to Landau damping, where the plasmon energy gives rise to the creation of electron-positron pairs. Read more
- Citation: arXiv:2201.10370v1

- Theoretical Studies of Long Lived Plasma Structures
- Authors: Maxim Dvornikov
- Published: 2010
- Summary: This paper constructs the model of a long-lived plasma structure based on spherically symmetric oscillations of electrons in plasma. It studies the interaction between electrons participating in spherically symmetric oscillations and finds that this interaction can be attractive, leading to bound states. Read more
- Citation: arXiv:1003.3660v1

- Electron gas oscillations in plasma. Theory and applications
- Authors: Maxim Dvornikov, Sergey Dvornikov
- Published: 2003
- Summary: This paper analyzes the solutions of the non-linear Schrödinger equation for spherically and axially symmetrical electrons density oscillations in plasma. It suggests that this mechanism could occur in nature as a rare phenomenon called the fireball and could be used in controlled fusion research. Read more
- Citation: arXiv:physics/0306157v2

- Neutral Plasma Oscillations at Zero Temperature
- Authors: S. D. Bergeson, R. L. Spencer
- Published: 2002
- Summary: This paper uses cold plasma theory to calculate the response of an ultracold neutral plasma to an applied rf field. It simulates plasma oscillations in an expanding ultracold neutral plasma, providing insights into the assumptions used to interpret experimental data. Read more
- Citation: arXiv:physics/0204084v1

**Quantum Mechanical Tunneling Theory in LENR**

Quantum Mechanical Tunneling Theory is a concept that has been explored in the context of Low Energy Nuclear Reactions (LENR). Here are some key research papers that delve into this theory:

- Quantum Tunneling in Breather Nano-colliders
- Authors: V. I. Dubinko
- Published: 2015-03-31
- Summary: This paper argues that discrete breathers (DBs) in crystals with sufficient anharmonicity can have a drastic effect on quantum tunneling. DBs present an efficient way to produce correlation effects, acting as breather nano-colliders (BNC) triggering LENR in solids. The tunneling probability for deuterium fusion in gap DBs is shown to increase drastically, resulting in observed LENR rates at extremely low concentrations of DBs.
- Link to paper

- Catalytic mechanism of LENR in quasicrystals based on localized anharmonic vibrations and phasons
- Authors: Volodymyr Dubinko, Denis Laptev, Klee Irwin
- Published: 2016-08-09
- Summary: This paper proposes a mechanism explaining the high catalytic activity of quasicrystals (QCs) based on localized anharmonic vibrations (LAVs) and phasons. The large amplitude atomic motion in LAVs and phasons results in time-periodic driving of adjacent potential wells occupied by hydrogen ions, leading to a drastic increase in the D-D or D-H fusion rate.
- Link to paper

- Tunneling in a quantum field theory on a compact one-dimensional space
- Authors: J. Baacke, N. Kevlishvili
- Published: 2005-05-13
- Summary: This paper computes tunneling in a quantum field theory in 1+1 dimensions for an asymmetric double well type. The study considers global tunneling and finds that tunneling occurs in a resonant way. The back-reaction of nonzero momentum modes can cause the potential barrier to disappear temporarily or indefinitely, replacing tunneling with a sliding of the wave function.
- Link to paper

- Real-Time Feynman Path Integral Realization of Instantons
- Authors: Aleksey Cherman, Mithat Unsal
- Published: 2014-07-31
- Summary: This paper explains how tunneling amplitudes are encoded in real-time Feynman path integrals. The essential steps are borrowed from Picard-Lefschetz theory and resurgence theory.
- Link to paper

- Quantum Tunneling In Deformed Quantum Mechanics with Minimal Length
- Authors: Xiaobo Guo, Bochen Lv, Jun Tao, Peng Wang
- Published: 2016-09-22
- Summary: This paper discusses quantum tunneling in deformed quantum mechanics with a minimal length. It derives a WKB connection formula through a turning point and uses it to calculate tunneling rates through potential barriers under the WKB approximation. The minimal length effects on quantum tunneling in nuclear and atomic physics are also discussed.
- Link to paper

**Nuclear Catalysis Theory**

Nuclear Catalysis Theory in the context of Low Energy Nuclear Reactions (LENR) has been explored in various studies. Here are some key papers that discuss this theory:

- Catalytic mechanism of LENR in quasicrystals based on localized anharmonic vibrations and phasons
- Authors: Volodymyr Dubinko, Denis Laptev, Klee Irwin
- Published: 2016-08-09
- Summary: This paper proposes a mechanism explaining the high catalytic activity of quasicrystals (QCs) based on unusual dynamics of atoms at special sites in QCs. The mechanism involves localized anharmonic vibrations (LAVs) and phasons, leading to a drastic increase in the D-D or D-H fusion rate. Link to paper

- Nuclear catalysis mediated by localized anharmonic vibrations
- Authors: Vladimir Dubinko
- Published: 2015-10-18
- Summary: This paper discusses the effect of Localized Anharmonic Vibrations (LAVs) on quantum tunneling and how they may act as breather nano-colliders catalyzing LENR in solids. The paper also proposes practical ways of catalyzing LENR based on special electromagnetic treatment or electron irradiation. Link to paper

- On the Nuclear Mechanisms Underlying the Heat Production by the E-Cat
- Authors: Norman D. Cook, Andrea Rossi
- Published: 2015-04-06
- Summary: This paper discusses the isotopic abundances found in the E-Cat reactor and argues that a major source of energy is a reaction between the first excited-state of Li-7 and a proton, followed by the breakdown of Be-8 into two alphas. The paper also speculates on similar mechanisms that may be involved in other LENR. Link to paper

- Magnetic catalysis in nuclear matter
- Authors: Alexander Haber, Florian Preis, Andreas Schmitt
- Published: 2014-09-01
- Summary: This paper explores the effect of a strong magnetic field on the chiral condensate at low temperatures, known as magnetic catalysis, and its impact on the transition between vacuum and nuclear matter. The study finds that the creation of nuclear matter in a strong magnetic field becomes energetically more costly. Link to paper

- Low energy nuclear reactions driven by discrete breathers
- Authors: Vladimir Dubinko
- Published: 2014-06-16
- Summary: This paper proposes a new mechanism of LENR in solids based on large amplitude anharmonic lattice vibrations, known as discrete breathers (DBs). The paper also discusses possible ways of engineering the nuclear active environment based on this concept. Link to paper

The main mathematical frameworks in these studies include the Schwinger model, Schrodinger equation for a particle in a non-stationary double well potential, and the lattice version of the independent-particle model (IPM) of nuclear theory.

**Electroweak Theory in LENR**

Electroweak Theory is a fundamental concept in particle physics that unifies the electromagnetic and weak forces. It’s not directly related to LENR, but some papers discuss various aspects of electroweak interactions. Below are some relevant papers:

- Varying Couplings in Electroweak Theory
- Authors: Douglas J. Shaw, John D. Barrow
- Published: 2004-12-30
- Summary: This paper extends the theory of Kimberly and Magueijo for the spacetime variation of the electroweak couplings in the unified Glashow-Salam-Weinberg model of the electroweak interaction to include quantum corrections. It derives the effective quantum-corrected dilaton evolution equations in the presence of a background cosmological matter density composed of weakly interacting and non-weakly-interacting non-relativistic dark-matter components.
- Link to paper

- Electroweak Physics: Summary
- Authors: Rupa Chatterjee
- Published: 2021-06-24
- Summary: This paper discusses electroweak probes as a potential tool to study the properties of the hot and dense strongly interacting matter produced in relativistic nuclear collisions due to their unique nature. It includes a selection of new experimental analysis and results from theory calculations on electromagnetic and weak probes.
- Link to paper

- The electroweak theory with a priori superluminal neutrinos and its physical consequences
- Authors: C. A. Dartora, G. G. Cabrera
- Published: 2011-12-13
- Summary: This paper explores the physical consequences of superluminal neutrinos described by a tachyonic Dirac Lagrangian within the standard model of electroweak interactions. It provides a simple explanation for the parity violation in weak interactions and why electroweak theory has a chiral aspect.
- Link to paper

- Electroweak Corrections and Unitarity in Linear Moose Models
- Authors: R. Sekhar Chivukula, Hong-Jian He, Masafumi Kurachi, Elizabeth H. Simmons, Masaharu Tanabashi
- Published: 2004-10-11
- Summary: This paper calculates the form of the corrections to the electroweak interactions in Higgsless models. It relates the size of corrections to electroweak processes to the spectrum of vector bosons (“KK modes”). The paper finds that Higgsless models with localized fermions are disfavored by precision electroweak data.
- Link to paper

- A geometry for the electroweak field
- Authors: Peter Morgan
- Published: 2003-02-07
- Summary: This paper suggests the structure of the electroweak theory by classical geometrical ideas. It constructs a nonlinear map from a 12-dimensional linear space of three Weyl spinors onto the 12-dimensional tangent bundle of the Stiefel manifold of orthonormal tetrads associated with the Lorentz group. The paper considers the electroweak field more natural than the Dirac field and suggests a path to bosonization of the electroweak field in (3+1) dimensions.
- Link to paper

**Collective Effects Theory**

Collective Effects Theory in the context of LENR is not directly addressed in the available literature. However, there are some works related to collective effects in different scientific domains. Here are some of them:

- Kinetic theory of two-dimensional point vortices with collective effects by Pierre-Henri Chavanis (Published: 2011-07-07)
- Summary: This paper develops a kinetic theory of point vortices in two-dimensional hydrodynamics, taking collective effects into account. It leads to a Lenard-Balescu-type kinetic equation for axisymmetric flows and discusses the scaling with N of the relaxation time for the system as a whole.
- Download PDF

- Collective Quantum Approach to Surface Plasmon Resonance Effect by M. Akbari-Moghanjoughi (Published: 2023-02-19)
- Summary: This research presents a theory of the surface plasmon resonance (SPR) effect based on the dual length-scale driven damped collective quantum oscillations of the spill-out electrons in plasmonic material surface. The resonance occurs when the wavenumber of the driving pseudo force matches that of the surface plasmon excitations.
- Download PDF

- Collective effects in emission of quantum dots strongly coupled to a microcavity photon by A. N. Poddubny, M. M. Glazov, N. S. Averkiev (Published: 2012-09-21)
- Summary: This paper presents a theory of non-linear emission of quantum dot ensembles coupled to the optical mode of the microcavity. It demonstrates that the nonlinearity due to the interaction strongly affects the shape of the emission spectra.
- Download PDF

- Theory of Vibrational Polariton Chemistry in the Collective Coupling Regime by Arkajit Mandal, Xinyang Li, Pengfei Huo (Published: 2021-07-09)
- Summary: This paper theoretically demonstrates that chemical reaction rate constant can be significantly suppressed by coupling molecular vibrations with an optical cavity, exhibiting both the collective coupling effect and the cavity-frequency modification of the rate constant.
- Download PDF

- Noise-induced Effects in Collective Dynamics and Inferring Local Interactions from Data by Jitesh Jhawar, Vishwesha Guttal (Published: 2019-11-21)
- Summary: This paper demonstrates a method to characterise the role of stochasticity directly from high-resolution time-series data of collective dynamics. It describes a method that enables connections between empirical data of animal (or cellular) collectives with the phenomenon of noise-induced states.
- Download PDF It’s worth noting that these papers do not directly relate to LENR but explore various aspects of collective effects in different scientific contexts.

**Nuclear Excitation by Electron Capture Theory**

The Nuclear Excitation by Electron Capture (NEEC) theory explores the resonant process where a continuum electron is captured into a bound state of an ion, simultaneously exciting the nucleus. This theory has been investigated in various contexts, including heavy ions, laser-assisted nuclear excitation, and plasma environments.

- Theory of nuclear excitation by electron capture for heavy ions
- Authors: Adriana Pálffy, Zoltán Harman, Werner Scheid
- Published: 2007
- Summary: Investigates the resonant process of NEEC in heavy ion collision systems using a Feshbach projection operator formalism and a nuclear collective model.
- Link to paper

- Theory of Laser-Assisted Nuclear Excitation by Electron Capture
- Authors: Pavlo Bilous
- Published: 2022
- Summary: Investigates the interplay of x-ray ionization and atomic and nuclear degrees of freedom in the process of laser-assisted NEEC, showing low excitation rates but strong enhancement with respect to direct two-photon nuclear excitation.
- Link to paper

- Nuclear excitation by electron capture in optical-laser-generated plasmas
- Authors: Jonas Gunst, Yuanbin Wu, Christoph H. Keitel, Adriana Pálffy
- Published: 2018
- Summary: Investigates NEEC in plasma environments generated by ultra-strong optical lasers, performing a comprehensive study of optimal parameters for efficient nuclear excitation.
- Link to paper

- Nuclear Excitation by Electron Capture in Excited Ions
- Authors: Simone Gargiulo, Ivan Madan, Fabrizio Carbone
- Published: 2021
- Summary: Shows that by considering the ion in an excited state prior to capture, new capture channels emerge, resulting in a boost of more than three orders of magnitude to the electron capture resonance strength.
- Link to paper

- Tailoring laser-generated plasmas for efficient nuclear excitation by electron capture
- Authors: Yuanbin Wu, Jonas Gunst, Christoph H. Keitel, Adriana Pálffy
- Published: 2017
- Summary: Investigates optimal parameters for NEEC in plasma environments generated by ultra-strong optical lasers, showing that experimental observation of nuclear excitation should be possible at current laser facilities.
- Link to paper

**Nuclear Excitation by Electron Transition Theory**

Nuclear Excitation by Electron Transition (NEET) is a process that has been explored in various contexts and theoretical models. Below are some key papers that discuss different aspects of this theory:

- Theory of the nuclear excitation by electron transition process near the K-edge by E. V. Tkalya (2006)
- Summary: A model is proposed for describing NEET near the-shell ionization threshold of an atom. The experimental results for theAu cross-section excitation are explained, and predictions are made forIr andOs. PDF

- Nuclear excitation by electron capture in optical-laser-generated plasmas by Jonas Gunst, Yuanbin Wu, Christoph H. Keitel, Adriana Pálffy (2018)
- Summary: This paper investigates the process of nuclear excitation by electron capture in plasma environments generated by ultra-strong optical lasers. The study considers the 4.85 keV nuclear excitation starting from the long-livedMo isomer. PDF

- Theory of nuclear excitation by electron capture for heavy ions by Adriana Pálffy, Zoltán Harman, Werner Scheid (2007)
- Summary: This paper investigates the resonant process of nuclear excitation by electron capture, where a continuum electron is captured into a bound state of an ion with simultaneous nuclear excitation. The cross-section is derived using a Feshbach projection operator formalism. PDF

- Nuclear excitation by two-photon electron transition by A. V. Volotka, A. Surzhykov, S. Trotsenko, G. Plunien, Th. Stöhlker, S. Fritzsche (2016)
- Summary: A new mechanism of nuclear excitation via two-photon electron transitions (NETP) is proposed and studied. The probability for such a two-photon decay via nuclear excitation is found to be comparable with other mechanisms. PDF

- Tailoring laser-generated plasmas for efficient nuclear excitation by electron capture by Yuanbin Wu, Jonas Gunst, Christoph H. Keitel, Adriana Pálffy (2017)
- Summary: This paper investigates the optimal parameters for nuclear excitation by electron capture in plasma environments generated by ultra-strong optical lasers. The study considers a 4.85 keV nuclear transition starting from the long-livedMo isomer. PDF

**Nuclear Isomer Theory**

Nuclear Isomer Theory deals with the study of isomeric states in nuclei, which are long-lived excited nuclear states. Different types of nuclear isomers exist, including spin isomer, K isomer, seniority isomers, and “shape and fission” isomer. The theory has been explored in various contexts and has applications in nuclear science and technology.

- Nuclear isomers: structures and applications
- Authors: Yang Sun, Michael Wiescher, Ani Aprahamian, Jacob L. Fisker
- Published: 2005
- Summary: This study focuses on isomeric states in nuclei along the rapid proton capture process path, emphasizing two waiting point nuclei Se-68 and Kr-72 characterized by shape coexistence. The impact of isomer states on isotopic abundance in X-ray bursts is also studied.
- Link to Paper

- Executive Summary of the Topical Program: Nuclear Isomers in the Era of FRIB
- Authors: G. W. Misch, M. R. Mumpower, F. G. Kondev, et al.
- Published: 2023
- Summary: This report outlines the many ways isomers influence and contribute to nuclear science and technology, especially in the four FRIB pillars. It concludes with a recommendation that the nuclear physics community actively pursue isomer research.
- Link to Paper

- Th isomer from a nuclear model perspective
- Authors: Nikolay Minkov, Adriana Pálffy
- Published: 2021
- Summary: This paper investigates the physical conditions for the emergence of the extremely low-lying nuclear isomerTh at approximately 8 eV. It explains the phenomenon as the result of a fine interplay between collective quadrupole-octupole and single-particle dynamics in the nucleus.
- Link to Paper

- Manipulation of Nuclear Isomers with Lasers: Mechanisms and Prospects
- Authors: Zhiguo Ma, Changbo Fu, Wanbing He, Yugang Ma
- Published: 2022
- Summary: This paper discusses the history and types of nuclear isomers, including spin isomer, K isomer, seniority isomers, and “shape and fission” isomer. It also explores the prospects of manipulating nuclear isomers with lasers.
- Link to Paper

- Astromers: Nuclear Isomers in Astrophysics
- Authors: G. Wendell Misch, Surja K. Ghorui, Projjwal Banerjee, Yang Sun, Matthew R. Mumpower
- Published: 2020
- Summary: This paper develops a method to compute thermally-mediated transition rates between the ground state and long-lived isomers in nuclei. It also establishes criteria for thermalization temperature and studies transitions in several isomers of likely astrophysical interest.
- Link to Paper

**Nuclear Lattice Energy Theory**

Nuclear Lattice Energy Theory is a complex approach that has been explored in various contexts. Here are some key papers that discuss different aspects of this theory:

- Nuclear Physics from Lattice Quantum Chromodynamics by Martin J. Savage (PDF) – Published on 2015-10-07. This paper discusses the state-of-the-art Lattice QCD calculations of quantities of interest in nuclear physics, progress that is expected in the near future, and the anticipated impact.
- Lattice QCD and nuclear physics for searches of physics beyond the Standard Model by Emanuele Mereghetti (PDF) – Published on 2018-12-28. This paper explores how the interplay of Lattice QCD and nuclear Effective Field Theories can lead to improved predictions for low-energy experiments, with controlled uncertainties.
- Nuclear Lattice Simulations with Chiral Effective Field Theory by Dean Lee, Bugra Borasoy, Thomas Schaefer (PDF) – Published on 2004-02-23. This paper studies nuclear and neutron matter by combining chiral effective field theory with non-perturbative lattice methods, providing a realistic simulation of many-body nuclear phenomena with no free parameters.
- Proton-proton fusion in lattice effective field theory by Gautam Rupak, Pranaam Ravi (PDF) – Published on 2014-11-10. This paper calculates the proton-proton fusion rate at low energy in a lattice effective field theory (EFT) formulation, treating the strong and the Coulomb interactions non-perturbatively.
- Lattice effective field theory for nuclei from A = 4 to A = 28 by Timo A. Lähde, Evgeny Epelbaum, Hermann Krebs, Dean Lee, Ulf-G. Meißner, Gautam Rupak (PDF) – Published on 2013-11-08. This paper presents an overview of the extension of Nuclear Lattice Effective Field Theory simulations to the regime of medium-mass nuclei, focusing on the determination of the ground-state energies of the alpha nuclei.

The mathematical frameworks used in these studies include Quantum Chromodynamics (QCD), chiral effective field theory, and lattice methods. These approaches allow for the exploration of nuclear interactions, structure, and reactions at various energy levels and densities.

**Nuclear Magnetic Resonance Theory**

Nuclear Magnetic Resonance (NMR) Theory is a well-studied field with various applications and interpretations. Here are some key papers and insights related to this theory:

- Theory of Nuclear Magnetic Relaxation in Haldane Gap Antiferromagnets
- Authors: Jacob Sagi, Ian Affleck
- Published: 1995
- Summary: A theory of NMR is developed for integer-spin, one-dimensional antiferromagnets, which exhibit the Haldane gap. Various approaches are considered, including free boson, free fermion, and non-linear sigma model, all of which give similar results. Detailed anisotropy and magnetic field dependence is calculated and compared with experiment. Link to paper

- Theory of NMR in semiconductor quantum point contact devices
- Authors: N. R. Cooper, V. Tripathi
- Published: 2007
- Summary: This paper describes how a local non-equilibrium nuclear polarization can be generated and detected by electrical means in a semiconductor quantum point contact device. It shows that measurements of the nuclear spin relaxation rate will provide clear signatures of the interaction mechanism underlying the “0.7” conductance anomaly. Link to paper

- Realization of generalized quantum searching using nuclear magnetic resonance
- Authors: Jingfu Zhang, Zhiheng Lu, Lu Shan, Zhiwei Deng
- Published: 2001
- Summary: The paper generalizes the quantum searching algorithm by replacing the Walsh-Hadamard transform with almost any quantum mechanical operation. The generalized algorithm is implemented using NMR techniques with chloroform molecules. Link to paper

- Nuclear magnetic resonances in (In,Ga)As/GaAs quantum dots studied by resonant optical pumping
- Authors: M. S. Kuznetsova, K. Flisinski, I. Ya. Gerlovin, M. Yu. Petrov, I. V. Ignatiev, S. Yu. Verbin, D. R. Yakovlev, D. Reuter, A. D. Wieck, M. Bayer
- Published: 2014
- Summary: This study explores the photoluminescence polarizations of quantum dots annealed at different temperatures as a function of external magnetic field. Resonant features appear due to all-optical NMR for optical excitation with modulated circular polarization. A theoretical model is developed to simulate quadrupole and Zeeman splittings of the nuclear spins in a strained quantum dot. Link to paper

- Quantum Computation Based on Magic-Angle-Spinning Solid State Nuclear Magnetic Resonance Spectroscopy
- Authors: Shangwu Ding, Charles A. McDowell, Chaohui Ye, Mingsheng Zhan, Xiwen Zhu, Kelin Gao, Xianping Sun, Xi-An Mao, Maili Liu
- Published: 2001
- Summary: This paper shows that magic-angle spinning (MAS) solid state NMR spectroscopy is a promising technique for implementing quantum computing. The theory underlying the principles of quantum computing with nuclear spin systems undergoing MAS is formulated in the framework of formalized quantum Floquet theory. Link to paper

**Nuclear Resonance Theory in LENR**

Nuclear Resonance Theory in the context of Low Energy Nuclear Reactions (LENR) has been explored by various researchers. Here are some key papers and their summaries:

- Enhancement Mechanisms of Low Energy Nuclear Reactions
- Authors: F. A. Gareev, I. E. Zhidkova
- Published: 2005
- Summary: This paper reviews possible stimulation mechanisms of LENR. It concludes that transmutation of nuclei at low energies and excess heat are possible within the framework of the universal resonance synchronization principle. The excitation and ionization of atoms may play a role as a trigger for LENR. Superlow energy of external fields may stimulate LENR. The results of this research field can provide a new source of energy, substances, and technologies. Link to paper

- Low energy nuclear reactions driven by discrete breathers
- Authors: Vladimir Dubinko
- Published: 2014
- Summary: This paper proposes a new mechanism of LENR in solids based on large amplitude anharmonic lattice vibrations, known as intrinsic localized modes or discrete breathers (DBs). Gap DBs in diatomic crystals such as metal hydrides are argued to be the LENR catalyzers. The large mass difference between H or D and the metal atoms provides a gap in the phonon spectrum, resulting in extreme dynamic closing of adjacent H/D atoms required for tunneling through the nuclear Coulomb barrier. Link to paper

- On low-energy nuclear reactions
- Authors: Péter Kálmán, Tamás Keszthelyi
- Published: 2019
- Summary: Based on recent theoretical findings, this paper shows that proton and deuteron capture reactions of extremely low energy may have accountable rates for all elements of the periodic table. It suggests a new way of thinking about LENR phenomena and provides possible explanations for contradictory observations and negative results of ‘cold fusion’ experiments. Link to paper

- New Cooperative Mechanisms of Low Energy Nuclear Reactions Using Superlow Energy External Fields
- Authors: F. A. Gareev, I. E. Zhidkova
- Published: 2005
- Summary: This paper proposes a new mechanism of LENR where cooperative processes in the whole system (nuclei, atoms, condensed matter) can occur at smaller threshold energies. The cooperative processes can be induced and enhanced by low energy external fields. The excess heat is the emission of internal energy, and transmutations at LENR are the result of redistribution of inner energy of the whole system. Link to paper

- Cooperative Enhancement Mechanisms of Low Energy Nuclear Reactions Using Superlow Energy External Fields
- Authors: F. A. Gareev, I. E. Zhidkova
- Published: 2006
- Summary: Similar to the previous paper, this work emphasizes the cooperative enhancement mechanisms of LENR using superlow energy external fields. It highlights the potential for LENR to occur at smaller threshold energies through cooperative processes. Link to paper

- Electromagnetic Meson Production in the Nucleon Resonance Region

Authors: V. D. Burkert, T. -S. H. Lee Published: 2004 Summary: This paper reviews recent experimental and theoretical advances in investigating electromagnetic meson production reactions in the nucleon resonance region. URL: Link to paper Mathematical Framework: Investigation of electromagnetic meson production.

7. Catalytic mechanism of LENR in quasicrystals based on localized anharmonic vibrations and phasons

- Authors: Volodymyr Dubinko, Denis Laptev, Klee Irwin
- Published: 2016-08-09
- Summary: The paper proposes a mechanism explaining the high catalytic activity of quasicrystals (QCs) based on unusual dynamics of atoms at special sites in QCs, namely, localized anharmonic vibrations (LAVs) and phasons. These large amplitude atomic motions result in time-periodic driving of adjacent potential wells occupied by hydrogen ions, leading to an increase in the fusion rate. Link to paper

- A model for enhanced fusion reaction in a solid matrix of metal deuterides
- Authors: K. P. Sinha, A. Meulenberg
- Published: 2009-01-16
- Summary: The study shows that the cross-section for fusion improves considerably if d-d pairs are located in linear chainlets or line defects in a solid matrix. The interaction with lattice vibrational modes causes localization of electron pairs on deuterons, leading to attraction of D+ D- pairs and strong screening of the nuclear repulsion. Link to paper

- Quantization of Differences Between Atomic and Nuclear Rest Masses and Selforganization of Atoms and Nuclei
- Authors: F. A. Gareev, I. E. Zhidkova
- Published: 2006-09-30
- Summary: The paper proposes a new mechanism of LENR based on cooperative processes in the whole system, including nuclei, atoms, and condensed matter. The cooperative resonance synchronization mechanisms are responsible for the explanation of how the electron volt world can influence the nuclear mega electron volt world. Link to paper

- Cooperative Enhancement Mechanisms of Low Energy Nuclear Reactions Using Superlow Energy External Fields

- Authors: F. A. Gareev, I. E. Zhidkova
- Published: 2006-01-05
- Summary: The paper proposes a cooperative enhancement mechanism of LENR, where cooperative processes in the whole system can occur at smaller threshold energies. These processes can be induced and enhanced by low energy external fields. Link to paper Note: The specific Widom-Larsen Theory was not found in the collected research, and the above papers provide related concepts and mechanisms in the field of LENR.

**Nuclear Spin Theory**

Authors: Various authors have contributed to the development of Nuclear Spin Theory in different contexts.

Citation:

- S. -I. Ando, Y. -H. Song, C. H. Hyun, K. Kubodera, “Spin Polarization inat Low Energies with a Pionless Effective Field Theory”, 2011.
- A. Deltuva, A. C. Fonseca, “Polarization observables and spin-aligned fusion rates in 2H(d,p)3H and 2H(d,n)3He reactions”, 2010.
- Yutaro Iizawa, Daisuke Jido, Takatsugu Ishikawa, “reaction for studying charge symmetry breaking in theinteraction”, 2022.
- C. R. Chinn, Ch. Elster, R. M. Thaler, S. P. Weppner, “Application of Multiple Scattering Theory to Lower Energy Elastic Nucleon-Nucleus Reactions”, 1994.
- Jun Xu, Bao-An Li, Wen-Qing Shen, Yin Xia, “Dynamical effects of spin-dependent interactions in low- and intermediate-energy heavy-ion reactions”, 2015.

Summary: Nuclear Spin Theory encompasses various studies and applications related to the spin of nucleons and its effects on nuclear reactions. Some key aspects include:

- Spin Polarization in Low Energies: This study focuses on the reaction ( \gamma d \to \vec{n}p ) for laboratory photon energy ranging from threshold to 30 MeV. The main goal is to calculate the neutron polarization and compare the results with experimental data.
- Polarization Observables in Deuteron-Deuteron Scattering: This research describes nucleon transfer reactions in low-energy deuteron-deuteron scattering, including the Coulomb interaction between protons.
- Charge Symmetry Breaking in the ( \Lambda N ) Interaction: This paper discusses charge symmetry breaking in the ( \Lambda N ) interaction and proposes reactions to investigate the ( \Lambda p ) and ( \Lambda n ) interactions at low energies.
- Multiple Scattering Theory in Nucleon-Nucleus Reactions: This work calculates the optical model potentials for nucleon-nucleus elastic scattering at 65 MeV for various nuclei, using first-order multiple scattering theory.
- Dynamical Effects of Spin-Dependent Interactions: This review summarizes the main physics motivations and recent progress in understanding spin dynamics and identifying spin-sensitive observables in heavy-ion reactions at intermediate energies.

Main Mathematical Frameworks:

- Pionless Effective Field Theory
- Momentum Space Equations
- Multiple Scattering Theory
- Time-Dependent Hartree-Fock Approach
- Transport Models

The Nuclear Spin Theory is a complex field that involves various mathematical and physical principles to understand the role of spin in nuclear reactions. It has applications in understanding nuclear structures, reactions, and dynamics, and continues to be an area of active research.

**Nuclear Structure Theory**

Nuclear Structure Theory focuses on the understanding of the structure and behavior of atomic nuclei. It is a rapidly evolving field that extends towards regions of exotic short-lived nuclei far from stability, nuclear astrophysics applications, and bridging the gap between low-energy QCD and the phenomenology of finite nuclei. The main objective is to build a consistent microscopic theoretical framework that provides a unified description of bulk properties, nuclear excitations, and reactions.

**Key Papers and Authors**

- Nuclear structure far from stability by D. Vretenar (2004)
- Summary: Review of recent theoretical advances in the description of structure phenomena in exotic nuclei far from stability.
- Download PDF

- Nuclear structure theory of the heaviest nuclei by A. V. Afanasjev, S. E. Agbemava (2016)
- Summary: Review of the application of covariant density functional theory to the description of actinides and superheavy nuclei.
- Download PDF

- From the liquid drop model to lattice QCD by V. Somà (2018)
- Summary: A concise account of the main developments in nuclear structure theory, from its origin in the 1930s to date, taking the modeling of inter-nucleon interactions as a guideline.
- Download PDF

- Towards a consistent approach to nuclear structure: EFT of two- and many-body forces by R. Machleidt, D. R. Entem (2005)
- Summary: Review of nuclear forces, including high-precision NN potentials and nuclear two- and many-body forces based on chiral effective field theory (EFT).
- Download PDF

- Nuclear shell structures in terms of classical periodic orbits by Ken-ichiro Arita (2016)
- Summary: Application of semiclassical periodic-orbit theory (POT) to the physics of nuclear structures, including the evolution of deformed shell structures and the effect of the spin degree of freedom.
- Download PDF

**Nuclear Theory**

Nuclear Theory is a broad field that encompasses various aspects of nuclear physics. Here are some key papers and insights related to this theory:

- A Vision for Nuclear Theory: Report to NSAC
- Authors: J. Carlson, B. Holstein, X. D. Ji, G. McLaughlin, B. Müller, W. Nazarewicz, K. Rajagopal, W. Roberts, X. -N. Wang
- Published: 2003
- Summary: This report reviews and evaluates current NSF and DOE supported efforts in nuclear theory and identifies strategic plans to ensure a strong U.S. nuclear theory program under various funding scenarios.
- Link to paper

- NUCLEAR THEORY WHITE PAPER 1995
- Authors: G. Bertsch, B. Mueller, J. Negele, J. Friar, V. Pandharipande
- Published: 1995
- Summary: This white paper reviews the accomplishments of nuclear theory during the past five years and identifies future challenges and research opportunities.
- Link to paper

- Overview and Perspectives in Nuclear Physics
- Authors: Wolfram Weise
- Published: 2008
- Summary: This presentation reviews recent guiding themes in nuclear physics, including developments in chiral effective field theory applied to nuclear systems, phases and structures of QCD, and matter under extreme conditions in heavy-ion collisions and neutron stars.
- Link to paper

- Nuclear matter properties, phenomenological theory of clustering at the nuclear surface, and symmetry energy
- Authors: Q. N. Usmani, Nooraihan Abdullah, K. Anwar, Zaliman Sauli
- Published: 2011
- Summary: This paper presents a phenomenological theory of nuclei that incorporates clustering at the nuclear surface. It explains the large symmetry energy at low densities of nuclear matter and is consistent with the static properties of nuclei.
- Link to paper

- From the liquid drop model to lattice QCD
- Authors: V. Somà
- Published: 2018
- Summary: This article gives a concise account of the main developments in nuclear structure theory, from its origin in the 1930s to date, taking the modeling of inter-nucleon interactions as a guideline.
- Link to paper

**Nuclear Transfer Reaction Theory**

Nuclear Transfer Reaction Theory is a concept that has been explored in various contexts within nuclear physics. Here are some key papers that discuss different aspects of this theory:

- Transfer Reactions in Nuclear Astrophysics
- Authors: Philip Adsley
- Published: 2022-12-07
- Summary: This paper outlines how transfer reactions may be used in nuclear astrophysics to identify states in nuclei and determine their contribution to astrophysical nuclear reactions. Link to paper

- Reaction mechanisms of pair transfer
- Authors: Ian J. Thompson
- Published: 2012-04-13
- Summary: This paper describes the mechanisms of nuclear transfer reactions for the transfer of two nucleons from one nucleus to another. It also discusses the interference between various simultaneous and sequential amplitudes. Link to paper

- Multinucleon transfer reaction in time-dependent Hartree-Fock theory
- Authors: Kazuyuki Sekizawa, Kazuhiro Yabana
- Published: 2015-11-26
- Summary: This paper investigates multinucleon transfer processes employing the Time-dependent Hartree-Fock theory and evaluates MNT cross sections for various reactions. Link to paper

- Single-Particle Transfer and Nuclear Supersymmetry. Pick-Up and Stripping with SUSY
- Authors: J. Barea, R. Bijker, A. Frank, G. Loyola
- Published: 2001-07-16
- Summary: This paper explores transfer reactions as a test for nuclear supersymmetry and constructs and evaluates one-nucleon transfer matrix elements between supersymmetric partners. Link to paper

- Single-particle spectroscopic strength from nucleon transfer reactions with a three-nucleon force contribution
- Authors: N. K. Timofeyuk, L. Moschini, M. Gómez-Ramos
- Published: 2023-03-02
- Summary: This paper points out the importance of a three-nucleon force in reactions with a loosely-bound projectile and studies its effects on nucleon transfer in various reactions. Link to paper

**Nuclear Transmutation Theory**

The Nuclear Transmutation Theory encompasses various aspects of nuclear reactions and transformations. Several studies have explored different facets of this theory:

- Theories of Low Energy Nuclear Transmutations by Y. N. Srivastava, A. Widom, J. Swain (2012): This paper shows that low energy nuclear reactions can be induced by all four fundamental interactions, including gravitational, strong, electromagnetic, and weak. The differences are highlighted through the diversity in the rates and similarity through the nature of the nuclear reactions initiated by each. Link to paper.
- Energetic Electrons and Nuclear Transmutations in Exploding Wires by A. Widom, Y. N. Srivastava, L. Larsen (2007): This study observes nuclear transmutations and fast neutrons emerging from large electrical current pulses passing through wire filaments. The nuclear reactions are explained as inverse beta transitions of energetic electrons absorbed by protons. The paper also discusses coherent collective motions of flowing electrons within a wire filament. Link to paper.
- Transmutation prospect of long-lived nuclear waste induced by high-charge electron beam from laser plasma accelerator by X. L. Wang et al. (2017): This paper demonstrates photo-transmutation of long-lived nuclear waste induced by high-charge relativistic electron beam from laser plasma accelerator. The study suggests that the laser-accelerated high-charge e-beam could be an efficient tool to transmute long-lived nuclear waste. Link to paper.
- Transmutations and spectral parameter power series in eigenvalue problems by Vladislav V. Kravchenko, Sergii M. Torba (2012): This paper provides an overview of recent developments in Sturm-Liouville theory concerning operators of transmutation and spectral parameter power series. It introduces systems of recursive integrals and the SPPS approach, explaining applications to spectral problems with numerical illustrations. Link to paper.

The main mathematical frameworks involved in these studies include the understanding of fundamental interactions, inverse beta transitions, coherent collective motions, and spectral parameter power series.

**Nuclear Vibrational Energy Theory**

The Nuclear Vibrational Energy Theory is a concept that has been explored in various contexts within nuclear physics. Here are some key studies related to this theory:

- Incorporating nuclear vibrational energies into the -atom in molecules- analysis: An analytical study
- Authors: Masumeh Gharabaghi, Shant Shahbazian
- Published: 2016
- Summary: This study develops the formalism of including nuclear vibrational energy in atomic basin energy within the context of the multi-component QTAIM (MC-QTAIM). It incorporates both electrons and quantum nuclei into the AIM analysis using non-adiabatic wavefunctions. The study demonstrates the quantum nuclei as quantum oscillators and computes the zero-point nuclear vibrational energy contribution to the basin energies explicitly. Link to paper

- Microscopic description of nuclear vibrations: Relativistic QRPA and its extensions with quasiparticle-vibration coupling
- Authors: Elena Litvinova, Victor Tselyaev
- Published: 2013
- Summary: This paper reviews the recent extensions of the covariant energy density functional theory with the quasiparticle-vibration coupling (QVC). It discusses the formulation of the Quasiparticle Random Phase Approximation (QRPA) in the relativistic framework and the implementation of QVC in two-body propagators in the nuclear medium. Link to paper

- Beyond the mean field in the particle-vibration coupling scheme
- Authors: M. Baldo, P. F. Bortignon, G. Colo’, D. Rizzo, L. Sciacchitano
- Published: 2015
- Summary: This paper presents a formal theory of the particle-vibration coupling model based on the Green’s function method. It extends to realistic effective forces the macroscopic particle-vibration coupling models and the Nuclear Field Theory. Link to paper

- Molecular vibrational frequencies from analytic Hessian of constrained nuclear-electronic orbital density functional theory
- Authors: Xi Xu, Yang Yang
- Published: 2021
- Summary: This study develops the analytic Hessian for constrained nuclear-electronic orbital density functional theory (cNEO-DFT) energy with respect to the change of nuclear positions. It characterizes stationary points on energy surfaces and computes molecular vibrational frequencies. Link to paper

- Particle-vibration coupling within covariant density functional theory
- Authors: E. Litvinova, P. Ring, V. Tselyaev
- Published: 2007
- Summary: This paper extends the covariant density functional theory to include Particle-Vibration Coupling (PVC) in a consistent way. It calculates the low-lying collective vibrations in Relativistic Random Phase Approximation (RRPA) and constructs an energy-dependent self-energy for the Dyson equation. Link to paper

**Nuclear Wave Function Theory**

Nuclear Wave Function Theory is a complex subject that has been explored in various contexts. Below are some key research papers related to this theory:

- Nuclear Wave Functions for Spin and Pseudospin Partners
- Authors: P. J. Borycki, J. Ginocchio, W. Nazarewicz, M. Stoitsov
- Published: 2003
- Summary: This paper investigates the effects of pseudospin and spin symmetry breaking on the single nucleon wave functions in spherical nuclei. It applies both relativistic and non-relativistic self-consistent models as well as the harmonic oscillator model. Link to paper

- Light Front Nuclear Theory and the HERMES Effect
- Authors: Gerald A. Miller
- Published: 2000
- Summary: This paper discusses the use of light cone variables to compute the nucleonic and mesonic components of nuclear wave functions. It covers various aspects including infinite nuclear matter, finite nuclei, nucleon-nucleon scattering, and nuclear saturation properties. Link to paper

- The anatomy of atomic nuclei: illuminating many-body wave functions through group-theoretical decomposition
- Authors: Calvin W. Johnson
- Published: 2017
- Summary: This paper explores the characterization of wavefunctions through irreducible representations of groups. It emphasizes using Lanczos-type methods to dissect arbitrary wavefunctions into group irreps, providing insights into nuclear wave functions. Link to paper

- New trial wave function for nuclear cluster structure of nuclei
- Authors: Bo Zhou
- Published: 2017
- Summary: This paper proposes a new trial wave function for nuclear physics, providing an exact solution to the center-of-mass problem. It applies this new wave function to study the(+) cluster system. Link to paper

- Inclusion of virtual nuclear excitations in the formulation of the (e,e’N)
- Authors: G. H. Rawitscher
- Published: 1998
- Summary: This paper presents a wave-function framework for the theory of the (e,e’N) reaction. It includes virtual nuclear excitations and uses coupled channel equations in the usual Feynman matrix element. Link to paper

The main mathematical frameworks involved in these studies include relativistic mean field theory, light cone variables, group-theoretical decomposition, and variational calculations with different cluster widths.

**Nuclear Weak Interaction Theory**

Nuclear Weak Interaction Theory explores weak interactions in nuclear systems, particularly at low energies. It has been studied in various contexts, including astrophysical processes, two-nucleon systems, and charge-exchange excitations.

- Astrophysical Weak-Interaction Processes and Nuclear Effective Field Theory
- Authors: K. Kubodera
- Published: 2004
- Summary: This paper presents a brief account of the basic features of the nuclear effective theory approach to low-energy nuclear weak-interaction processes in astrophysical contexts. Link to paper

- Hadronic Weak Interaction in the Two-Nucleon System with Effective Field Theories
- Authors: Shung-ichi Ando, Chang Ho Hyun, Jae Won Shin
- Published: 2010
- Summary: This paper explores weak interactions in the two-nucleon system at low energies using effective field theory. It reviews calculations of parity-violating observables in radiative neutron capture on a proton. Link to paper

- Modeling Nuclear Weak-Interaction Processes with Relativistic Energy Density Functionals
- Authors: N. Paar, T. Marketin, D. Vale, D. Vretenar
- Published: 2015
- Summary: This paper reviews recent developments in modeling nuclear weak-interaction processes, including charge-exchange excitations and charged-current neutrino-nucleus reactions. Link to paper

- Nuclear Charge-Exchange Excitations Based on Relativistic Density-Dependent Point-Coupling Model
- Authors: D. Vale, Y. F. Niu, N. Paar
- Published: 2020
- Summary: This paper investigates spin-isospin transitions in nuclei using the proton-neutron relativistic quasiparticle random phase approximation. It provides insight into weak interaction processes in stellar environments. Link to paper

- Parity-Violating Polarization inwith a Pionless Effective Field Theory
- Authors: J. W. Shin, S. Ando, C. H. Hyun
- Published: 2009
- Summary: This paper considers the two-nucleon weak interaction with a pionless effective field theory and applies the model to the calculation of a parity-violating observable in neutron-proton capture at threshold. Link to paper

**Nucleon Cluster Model Theory**

The Nucleon Cluster Model Theory is a concept used in nuclear physics to describe the interactions and structure of nucleons (protons and neutrons) within a nucleus. Several research papers have explored this theory from different perspectives:

- A microscopic cluster model study ofHe+scatterings by K. Arai, S. Aoyama, Y. Suzuki (2008) [Link]: This study calculatesHe+scattering phase shifts in two different microscopic cluster models, Model T and Model C, to show the effects of tensor force and-wave components in the cluster wave function. Model T employs a realistic nucleon-nucleon potential and includes the-wave, whereas Model C considers the tensor-force effect to be renormalized into the central force.
- Nucleon clustering at kinetic freezeout of heavy-ion collisions via path-integral Monte Carlo by Dallas DeMartini, Edward Shuryak (2020) [Link]: This paper studies clustering of the four-nucleon system at kinetic freezeout conditions using path-integral Monte Carlo techniques. It provides estimates for decay probabilities of the 4N system into various light nuclei decay channels and characterizes the strength of spatial correlations.
- Ab initio coupled-cluster approach to nuclear structure with modern nucleon-nucleon interactions by G. Hagen, T. Papenbrock, D. J. Dean, M. Hjorth-Jensen (2010) [Link]: This research performs coupled-cluster calculations for various nuclei and employs both bare and secondary renormalized nucleon-nucleon interactions. It explores the validity of power counting estimates in medium-mass nuclei and the missing contributions due to three-nucleon forces.
- Nuclear Clustering in Fermionic Molecular Dynamics by Hans Feldmeier, Thomas Neff (2016) [Link]: This paper discusses the role of clustering in nuclear structure, especially for light nuclei in the-shell. It presents Fermionic Molecular Dynamics (FMD) as a microscopic many-body approach that includes clustering dynamically.
- Antisymmetrization in the Multicluster Dynamic Model of Nuclei and the Nucleon Exchange Effects by R. A. Eramzhyan, G. G. Ryzhikh, Yu. M. Tchuvil’sky (1997) [Link]: This paper proposes a modified version of the Multicluster Dynamic Model of nuclei to construct completely antisymmetrized wave functions of multicluster systems. It applies the model to six-nucleon systems and calculates various static and dynamic characteristics.

The mathematical frameworks used in these studies include microscopic cluster models, path-integral Monte Carlo techniques, coupled-cluster calculations, and Fermionic Molecular Dynamics. The theory helps in understanding the clustering effects in nuclear structure and reactions.

**Nucleon Pairing Theory**

The Nucleon Pairing Theory explores the pairing properties of nucleonic matter, including the off-shell propagation associated with short-range and tensor correlations. Several aspects of this theory have been studied by different researchers.

- Pairing in Nuclei by Wojciech Satula (link): This paper discusses simple generic aspects of nuclear pairing in a homogeneous medium and finite nuclei. It argues that low-energy nuclear structure is not sensitive enough to resolve fine details of nuclear nucleon-nucleon (NN) interaction in general and pairing NN interaction in particular. This allows for regularization of the ultraviolet (high-momentum) divergences and a consistent formulation of effective superfluid local theory (PDF).
- The BCS theory of q-deformed nucleon pairs – qBCS by S. Shelly Sharma, N. K. Sharma (link): This paper constructs a coherent state of q-deformed zero coupled nucleon pairs distributed in several single-particle orbits. The study of Sn isotopes reveals a well-defined universe of (G, q) values, for which qBCS converges. The pairing correlations in N nucleon system increase with increasing q (for q real) (PDF).
- Nuclear pairing from chiral pion-nucleon dynamics by N. Kaiser, T. Niksic, D. Vretenar (link): This paper uses a recently improved version of the chiral nucleon-nucleon potential to calculate thepairing gap in isospin-symmetric nuclear matter. The inclusion of the two-pion exchange reduces substantially the cut-off dependence of thepairing gap (PDF).
- Pairing properties of nucleonic matter employing dressed nucleons by H. Müther, W. H. Dickhoff (link): This paper presents a survey of pairing properties of nucleonic matter that includes the off-shell propagation associated with short-range and tensor correlations. A huge reduction in the strength as well as temperature and density range of-pairing is obtained for nuclear matter as compared to the standard BCS treatment (PDF).
- Nucleon-pair approximation with matrix representation by Y. Lei, Y. Lu, Y. M. Zhao (link): This paper proposes an approach of the nucleon-pair approximation (NPA), in which the collective nucleon pairs are represented in terms of antisymmetric matrices. The present approach significantly simplifies the NPA computation and is formulated on the same footing with and without isospin (PDF).

**Nucleon Transfer Reaction Theory**

The Nucleon Transfer Reaction Theory has been explored in various contexts and frameworks. Here are some key studies:

- Mass dispersion in transfer reactions with a stochastic mean-field theory
- Authors: Kouhei Washiyama, Sakir Ayik, Denis Lacroix
- Published: 2009
- Summary: Investigates nucleon transfer in symmetric heavy-ion reactions at energies below the Coulomb barrier using a microscopic stochastic mean-field theory. The approach provides a fully microscopic theory consistent with the phenomenological analysis of experimental data. Link

- Multinucleon transfer reaction in time-dependent Hartree-Fock theory
- Authors: Kazuyuki Sekizawa, Kazuhiro Yabana
- Published: 2015
- Summary: Investigates multinucleon transfer processes employing Time-dependent Hartree-Fock theory. A particle-number projection method is developed to calculate transfer probabilities and excitation energies. Link

- Theory of doorway states for one-nucleon transfer reactions
- Authors: B. L. Birbrair, V. I. Ryazanov
- Published: 1999
- Summary: Discusses the doorway states for one-nucleon transfer reactions, carrying important information about both nuclear structure and free-space nucleon-nucleon interaction. Link

- Single-particle spectroscopic strength from nucleon transfer reactions with a three-nucleon force contribution
- Authors: N. K. Timofeyuk, L. Moschini, M. Gómez-Ramos
- Published: 2023
- Summary: Points out that in reactions with a loosely-bound projectile, an additional three-body force arises, affecting nucleon transfer in various reactions. The study bridges nuclear structure theory and nuclear direct reaction theory. Link

- One-nucleon transfer reactions and the optical potential
- Authors: F. M. Nunes, A. Lovell, A. Ross, L. J. Titus, R. J. Charity, W. H. Dickhoff, M. H. Mahzoon, J. Sarich, S. M. Wild
- Published: 2015
- Summary: Provides a summary of new developments in direct reaction theory with a focus on one-nucleon transfer reactions, discussing the effects of nonlocality in the optical potential. Link

**Nucleon Transmutation Theory**

The Nucleon Transmutation Theory encompasses a range of phenomena where nucleons (protons and neutrons) can be transformed into one another under various physical conditions. Several studies have explored different aspects of nucleon transmutation:

- Theories of Low Energy Nuclear Transmutations by Y. N. Srivastava, A. Widom, J. Swain (2012): This paper shows that low energy nuclear reactions can be induced by all four fundamental interactions, including gravitational, strong, electromagnetic, and weak forces. Link to paper.
- Energetic Electrons and Nuclear Transmutations in Exploding Wires by A. Widom, Y. N. Srivastava, L. Larsen (2007): This study explains nuclear transmutations and fast neutrons emerging from large electrical current pulses passing through wire filaments. The nuclear reactions are explained as inverse beta transitions of energetic electrons absorbed by protons. Link to paper.
- Photofission and Quasi-Deuteron-Nuclear State as Mixing of Bosons and Fermions by G. Kaniadakis, A. Lavagno, P. Quarati (1996): This paper theoretically justifies the empirical-phenomenological quasi-deuteron photofission description within the semiclassical, intermediate statistics model. Link to paper.
- Fermion transmutation – a renormalization effect in gauge theory by S. T. Tsou, H. M. Chan (2000): This paper predicts a new category of phenomena where fermions of different flavours can transmute into one another as a consequence of the ‘rotating’ mass matrix due to renormalization. Link to paper.
- Quantum mechanical description of excitation energy distribution of the reaction residue in nucleon-induced inclusive one-nucleon knockout reactions by Kazuyuki Ogata (2018): This paper focuses on understanding inclusive one-nucleon knockout reactions for long-lived fission fragments (LLFPs), crucial for nuclear transmutation studies. Link to paper.

The main mathematical frameworks vary across these studies, including semiclassical models, quantum mechanical descriptions, and gauge theory. The diversity in the rates and similarity in the nature of the nuclear reactions initiated by each interaction is a common theme across these works.

**Nucleon Vibrational Energy Theory**

The Nucleon Vibrational Energy Theory explores the vibrational correlation energy and dynamics in nuclear systems. It has been studied in various contexts, including the pairing excitations of nuclei, the effects of meson-nucleon dynamics, and the temperature evolution of nuclear shell structure.

- Closed expression for the pair vibrational correlation energy of a uniform distribution of single-nucleon levels
- Authors: K. Neergård
- Published: 2016
- Summary: A closed expression is derived for the pair vibrational correlation energy generated in the random phase approximation by the isovector pairing force. Applications to the analysis of the symmetry energy of the isovector pairing model and to a Strutinskij renormalization of this model are discussed. Link to paper

- Excitation of monopole pairing vibrations in two-neutron transfer reaction: a semiclassical approach
- Authors: V. I. Abrosimov, A. I. Levon
- Published: 2019
- Summary: A simple model of monopole pairing excitations in superfluid nuclei is considered. The ratio of the spectroscopic factor for the excitation of monopole pairing vibrations in the (p,t) reaction in even superfluid nuclei to the spectroscopic factor for the transfer of two neutrons to the ground state is estimated. Link to paper

- Effects of meson-nucleon dynamics in a relativistic approach to medium-mass nuclei
- Authors: Elena Litvinova, Caroline Robin
- Published: 2017
- Summary: This paper reviews recent developments in the relativistic nuclear field theory (RNFT), including the impact of isospin dynamics on the nuclear shell structure and the isospin-flip pairing vibrations. Link to paper

- Temperature evolution of the nuclear shell structure and the dynamical nucleon effective mass
- Authors: Herlik Wibowo, Elena Litvinova, Yinu Zhang, Paolo Finelli
- Published: 2020
- Summary: The study investigates the fragmentation of the single-particle states and its evolution with temperature for the nuclear systems relevant for the core-collapse supernova. Link to paper

- Quasiparticle-vibration coupling in relativistic framework: shell structure of Z=120 isotopes
- Authors: Elena Litvinova
- Published: 2011
- Summary: This paper describes the shell structure of open-shell nuclei in a fully self-consistent extension of the covariant energy density functional theory, including the shell evolution in superheavy isotopes. Link to paper

**Nucleon Wave Function Theory**

The Nucleon Wave Function Theory has been explored in various contexts and models. Below are some key contributions:

- Covariant nucleon wave function with S, D, and P-state components
- Authors: Franz Gross, G. Ramalho, M. T. Pena
- Published: 2012
- Summary: Expressions for the nucleon wave functions in the covariant spectator theory (CST) are derived. The nucleon is described as a system with an off-mass-shell constituent quark, free to interact with an external probe, and two spectator constituent quarks on their mass shell. The derived nucleon wave function includes contributions from S, P, and D-waves. Link to paper

- Antisymmetrized, translationally invariant theory of the nucleon optical potential
- Authors: R. C. Johnson
- Published: 2019
- Summary: This work defines a nucleon optical model wave function as a projection of a many-nucleon scattering state within a translationally invariant second quantized many-body theory. The resulting optical model operator satisfies the requirements of rotational and translational invariance. Link to paper

- Light cone nucleon wave function in the quark-soliton model
- Authors: V. Yu. Petrov, M. V. Polyakov
- Published: 2003
- Summary: The light-cone wave function of the nucleon is calculated in the quark-soliton model inspired by the theory of the instanton vacuum of QCD. The nucleon wave function for large N_c can be expressed in terms of the wave function of the discrete level in the self-consistent meson field and light cone wave functions of 1,2, etc mesons. Link to paper

- Nuclear Wave Functions for Spin and Pseudospin Partners
- Authors: P. J. Borycki, J. Ginocchio, W. Nazarewicz, M. Stoitsov
- Published: 2003
- Summary: This study investigates the effects of pseudospin and spin symmetry breaking on the single nucleon wave functions in spherical nuclei, applying both relativistic and non-relativistic self-consistent models as well as the harmonic oscillator model. Link to paper

- Theoretical description of three- and four-nucleon scattering states using bound-state-like wave functions
- Authors: A. Kievsky, M. Viviani, L. E. Marcucci
- Published: 2011
- Summary: Bound-state-like wave functions are used to determine the scattering matrix corresponding to low energy N-d and p-^3He collisions. The construction of degenerate bound-state-like wave functions belonging to the continuum spectrum of the Hamiltonian is discussed. Link to paper

**Nucleon Weak Interaction Theory**

The Nucleon Weak Interaction Theory explores weak interactions within the two-nucleon system at low energies, often within the framework of effective field theory. Several aspects of this theory have been studied, including the application of Effective Field Theory (EFT) to the Nucleon-Nucleon (NN) interaction, parity-violating observables in radiative neutron capture on a proton, and the quenching of weak interactions in nucleon matter.

- Chiral Symmetry and the Nucleon Nucleon Interaction by Keith G. Richardson, published in 2000, explores the application of EFT to the NN interaction, considering contributions beyond One Pion Exchange predicted by Chiral Symmetry. Read more PDF.
- Hadronic weak interaction in the two-nucleon system with effective field theories by Shung-ichi Ando, Chang Ho Hyun, Jae Won Shin, published in 2010, reviews calculations of parity-violating observables in radiative neutron capture on a proton at threshold. Read more PDF.
- Parity-violating polarization inwith a pionless effective field theory by J. W. Shin, S. Ando, C. H. Hyun, published in 2009, considers the two-nucleon weak interaction with a pionless effective field theory. Read more PDF.
- Quenching of Weak Interactions in Nucleon Matter by S. Cowell, V. R. Pandharipande, published in 2002, calculates the one-body Fermi and Gamow-Teller charge-current, and vector and axial-vector neutral-current nuclear matrix elements in nucleon matter. Read more PDF.
- Reduction of Weak Interaction Rates in Neutron Stars by Nucleon Spin Fluctuations: Degenerate Case by Georg Raffelt, Thomas Strobel, published in 1996, studies nucleon spin fluctuations in a dense medium and their effect on weak interaction rates. Read more PDF.

The main mathematical frameworks involved in these studies include Effective Field Theory, Chiral Symmetry, and various calculations related to weak interactions, scattering, and spin fluctuations.

**Nucleus Cluster Model Theory**

The Nucleus Cluster Model Theory explores the possibility of certain clusters being the basic building blocks of medium mass nuclei. The theory has been discussed in various contexts and frameworks.

- The possibility ofC cluster as a building block of medium mass nuclei
- Authors: N. Itagaki, A. V. Afanasjev, D. Ray
- Published: 2019
- Summary: This paper discusses theC cluster as a basic building block of medium mass nuclei. The authors explore theC+C structure inMg using antisymmetrized quasi-cluster model (AQCM) and cranked relativistic mean field (CRMF) calculations. The existence of linear chain threeC cluster structure inAr has also been predicted.
- Mathematical Framework: AQCM, CRMF

- The pseudo-Semimicroscopic Algebraic Cluster Model model: Heavy nuclei
- Authors: Huitzilin Yépez-Martínez, Peter O. Hess
- Published: 2017
- Summary: The paper extends the Semimicroscopic Algebraic Cluster Model (SACM) to heavy nuclei using the pseudo-SU(3) model. The model is applied to 236U210Pb+26Ne and 224Ra $\rightarrow} 210Pb+14C, calculating some spectroscopic factors.
- Mathematical Framework: SACM, pseudo-SU(3)

- Dinuclear concept – cluster model of fusion
- Authors: G. G. Adamian, N. V. Antonenko, E. A. Cherepanov, A. K. Nasirov, W. Scheid, V. V. Volkov
- Published: 1999
- Summary: This paper analyzes the synthesis of superheavy elements within the dinuclear system concept of compound nucleus formation.
- Mathematical Framework: Dinuclear system concept

- Analysis of clustering phenomena in ab initio approaches
- Authors: D. M. Rodkin, Yu. M. Tchuvil’sky
- Published: 2018
- Summary: The paper devises an approach for explicit consideration of cluster effects in nuclear systems and accurate ab initio calculations of cluster characteristics of nuclei, including the 8Be nucleus.
- Mathematical Framework: No-Core Shell Model, translationally-invariant wave functions

- Coupling dynamical and statistical mechanisms for baryonic cluster production in nucleus collisions of intermediate and high energies
- Authors: A. S. Botvina, N. Buyukcizmeci, M. Bleicher
- Published: 2020
- Summary: This paper explores the production of baryonic clusters in central nucleus-nucleus collisions, considering the formation of primary diluted excited baryon clusters and their statistical decay. The paper also suggests a generalization of such a clusterization mechanism for hypernuclear matter.
- Mathematical Framework: Dynamical and statistical mechanisms

**Nucleus Pairing Theory**

The Nucleus Pairing Theory explores the pairing transition in nuclei, particularly focusing on the transition from superfluid to normal states. Several studies have investigated this phenomenon using different approaches and models.

- Thermodynamics of pairing transition for Odd-A nuclei
- Authors: Tao Yan, Yanlong Lin, Lang Liu
- Published: 2021
- Summary: Investigated the hot nucleusYb using covariant density functional theory with the PC-PK1 effective interaction. The study explored the S-shaped heat capacity ofYb in terms of blocking effect, single-particle levels, pairing gap, and defined seniority components. The pairing transition from the superfluid state to the normal state was also analyzed.
- Link to paper

- Pairing transition of nuclei at finite temperature
- Authors: K. Kaneko, M. Hasegawa
- Published: 2004
- Summary: Investigated pairing transition at finite temperature using shell model and BCS calculations. The study identified a “transition temperature” estimated from a “thermal” odd-even mass difference and found that the critical temperature increases with increasing deformation.
- Link to paper

- Classification of pairing phase transition in the hot nucleus
- Authors: Yuhang Gao, Yanlong Lin, Lang Liu
- Published: 2023
- Summary: Investigated the hot nucleususing covariant density functional theory, where the shell-model-like approach treats the pairing correlation. The study applied Lee-Yang’s theorem to classify the pairing phase transition and determined the first order of the phase transition near the critical temperature.
- Link to paper

- Finite temperature pairing re-entrance in drip-lineNi nucleus
- Authors: M. Belabbas, J. J. Li, J. Margueron
- Published: 2017
- Summary: PredictedNi as a possible candidate for the finite temperature pairing re-entrance phenomenon. The study showed that pairing re-entrance modifies the proton single particle energies around the Fermi level, as well as occupation numbers, and quasi-particle levels.
- Link to paper

- Pairing gaps from nuclear mean-field models
- Authors: M. Bender, K. Rutz, P. -G. Reinhard, J. A. Maruhn
- Published: 2000
- Summary: Discussed the pairing gap in chains of spherical, semi-magic nuclei using self-consistent nuclear mean-field models. The study compared experimental values for the pairing gap with calculations employing both a delta pairing force and a density-dependent delta interaction in the BCS and Lipkin-Nogami model.
- Link to paper

**Nucleus Transfer Reaction Theory**

Overview:

Nucleus Transfer Reaction Theory describes the process of transferring nucleons (protons or neutrons) between atomic nuclei during a nuclear reaction. It’s essential in understanding nuclear reactions in both astrophysical and laboratory contexts.

Relevant Authors, Research Papers, and Links:

- Neutron transfer reactions in halo effective field theory
- Authors: M. Schmidt, L. Platter, H. -W. Hammer
- Link to Paper
- Download PDF
- Published: 2018-12-21

- Reaction mechanisms of pair transfer
- Authors: Ian J. Thompson
- Link to Paper
- Download PDF
- Published: 2012-04-13

- Pairing interaction and two-nucleon transfer reactions
- Authors: Gregory Potel, Andrea Idini, Francisco Barranco, Enrico Vigezzi, Ricardo A. Broglia
- Link to Paper
- Download PDF
- Published: 2014-04-04

- Neutron transfer reactions in accreting neutron stars
- Authors: Andrey I. Chugunov
- Link to Paper
- Download PDF
- Published: 2018-11-21

- Analysis of two-nucleon transfer reactions in the 20Ne + 116Cd system at 306 MeV
- Authors: D. Carbone, J. L. Ferreira, S. Calabrese, F. Cappuzzello, M. Cavallaro, A. Hacisalihoglu, H. Lenske, J. Lubian, R. I. Magana Vsevolodovna, E. Santopinto, C. Agodi, L. Acosta, D. Bonanno, T. Borello-Lewin, I. Boztosun, G. A. Brischetto, S. Burrello, D. Calvo, E. R. Chávez Lomelí, I. Ciraldo, M. Colonna, F. Delaunay, N. Deshmukh, P. Finocchiaro, M. Fisichella, A. Foti, G. Gallo, F. Iazzi, L. La Fauci, G. Lanzalone, R. Linares, N. H. Medina, M. Moralles, J. R. B. Oliveira, A. Pakou, L. Pandola, H. Petrascu, F. Pinna, S. Reito, G. Russo, O. Sgouros, S. O. Solakci, V. Soukeras, G. Souliotis, A. Spatafora, D. Torresi, S. Tudisco, A. Yildirin, V. A. B. Zagatto
- Link to Paper
- Download PDF
- Published: 2021-10-20

**Nucleus Transmutation Theory**

Overview:

Nucleus Transmutation Theory refers to the conversion of one chemical element or isotope into another through nuclear reactions. It’s a subject of interest in nuclear physics and has applications in nuclear medicine and energy production.

Relevant Authors, Research Papers, and Links:

- Theories of Low Energy Nuclear Transmutations
- Authors: Y. N. Srivastava, A. Widom, J. Swain
- Link to Paper
- Download PDF
- Published: 2012-10-27

- Energetic Electrons and Nuclear Transmutations in Exploding Wires
- Authors: A. Widom, Y. N. Srivastava, L. Larsen
- Link to Paper
- Download PDF
- Published: 2007-09-08

- Characterization of specific nuclear reaction channels by deconvolution in the energy space of the total nuclear cross-section of protons – applications to proton therapy and technical problems (transmutations)
- Authors: W. Ulmer
- Link to Paper
- Download PDF
- Published: 2016-04-28

- Fusion Driven Transmutation of Transuranics in a Molten Salt
- Authors: Joshua Tanner, Ales Necas, Sydney Gales, Gerard Mourou, Toshiki Tajima
- Link to Paper
- Download PDF
- Published: 2021-09-17

- Neutron Production Rates by Inverse-Beta Decay in Fully Ionized Plasmas
- Authors: L. Maiani, A. D. Polosa, V. Riquer
- Link to Paper
- Download PDF
- Published: 2014-01-21

**Nucleus Vibrational Energy Theory**

Overview:

Nucleus Vibrational Energy Theory explores the vibrational motions within the nucleus, considering both collective excitations and interactions between nucleons. It has applications in understanding nuclear structure, reactions, and bonding properties.

Relevant Authors, Research Papers, and Links:

- Incorporating nuclear vibrational energies into the -atom in molecules- analysis: An analytical study
- Authors: Masumeh Gharabaghi, Shant Shahbazian
- Link to Paper
- Download PDF
- Published: 2016-11-14

- Effective field theory for vibrations in odd-mass nuclei
- Authors: E. A. Coello Pérez, T. Papenbrock
- Link to Paper
- Download PDF
- Published: 2016-08-09

- A microscopic nuclear collective rotation-vibration model: 2D submodel
- Authors: Parviz Gulshani
- Link to Paper
- Download PDF
- Published: 2016-02-03

- Nucleus-electron correlation revising molecular bonding fingerprints from the exact wavefunction factorization
- Authors: Ziyong Chen, Jun Yang
- Link to Paper
- Download PDF
- Published: 2021-04-09

- Excitation of monopole pairing vibrations in two-neutron transfer reaction: a semiclassical approach
- Authors: V. I. Abrosimov, A. I. Levon
- Link to Paper
- Download PDF
- Published: 2019-12-23

**Nucleus Vibrational Energy Theory**

Overview:

Nucleus Vibrational Energy Theory explores the vibrational energy of atomic nuclei and its implications in nuclear physics. This theory has been instrumental in understanding collective excitations in nuclei and has applications in various fields such as molecular bonding and nuclear reactions.

Relevant Authors, Research Papers, and Links:

- Incorporating nuclear vibrational energies into the -atom in molecules- analysis: An analytical study
- Authors: Masumeh Gharabaghi, Shant Shahbazian
- Link to Paper
- Download PDF
- Published: 2016-11-14

- Effective field theory for vibrations in odd-mass nuclei
- Authors: E. A. Coello Pérez, T. Papenbrock
- Link to Paper
- Download PDF
- Published: 2016-08-09

- A microscopic nuclear collective rotation-vibration model: 2D submodel
- Authors: Parviz Gulshani
- Link to Paper
- Download PDF
- Published: 2016-02-03

- Nucleus-electron correlation revising molecular bonding fingerprints from the exact wavefunction factorization
- Authors: Ziyong Chen, Jun Yang
- Link to Paper
- Download PDF
- Published: 2021-04-09

- Excitation of monopole pairing vibrations in two-neutron transfer reaction: a semiclassical approach
- Authors: V. I. Abrosimov, A. I. Levon
- Link to Paper
- Download PDF
- Published: 2019-12-23

**Nucleus Wave Function Theory**

Overview:

Nucleus Wave Function Theory deals with the mathematical description of the wave function of a nucleus, which encapsulates information about the quantum state of the system. This theory has applications in understanding nuclear structure, reactions, and interactions.

Relevant Authors, Research Papers, and Links:

- New trial wave function for nuclear cluster structure of nuclei
- Authors: Bo Zhou
- Link to Paper
- Download PDF
- Published: 2017-11-20

- On the dependence of the wave function of a bound nucleon on its momentum and the EMC effect
- Authors: C. Ciofi degli Atti, L. L. Frankfurt, L. P. Kaptari, M. I. Strikman
- Link to Paper
- Download PDF
- Published: 2007-06-20

- Inclusion of virtual nuclear excitations in the formulation of the (e,e’N)
- Authors: G. H. Rawitscher
- Link to Paper
- Download PDF
- Published: 1998-02-07

- Resonance State Wave Functions ofBe using Supersymmetric Quantum Mechanics
- Authors: S. K. Dutta, D. Gupta, Swapan K. Saha
- Link to Paper
- Download PDF
- Published: 2017-03-28

- On the Relativistic Description of the Nucleus
- Authors: R. Cenni, G. Vagradov
- Link to Paper
- Download PDF
- Published: 2005-04-01

**Nucleus Weak Interaction Theory**

Overview:

Nucleus Weak Interaction Theory focuses on the weak interaction processes within the nucleus, including beta-decay, electron capture, and neutrino-nucleus reactions. This theory has applications in astrophysics, dark matter detection, and understanding the fundamental forces in the nucleus.

Relevant Authors, Research Papers, and Links:

- Modeling nuclear weak-interaction processes with relativistic energy density functionals
- Authors: N. Paar, T. Marketin, D. Vale, D. Vretenar
- Link to Paper
- Download PDF
- Published: 2015-05-27

- Coherence in scattering of massive weakly interacting neutral particles off nuclei
- Authors: V. A. Bednyakov
- Link to Paper
- Download PDF
- Published: 2023-02-22

- The Renormalized Tensor Interaction in a Nucleus
- Authors: S. J. Q. Robinson L. Zamick
- Link to Paper
- Download PDF
- Published: 2007-09-20

- Contribution of excited states to stellar weak-interaction rates in odd-A nuclei
- Authors: Pedro Sarriguren
- Link to Paper
- Download PDF
- Published: 2016-05-09

- Weak response of nuclei
- Authors: A. Botrugno, G. Co’
- Link to Paper
- Download PDF
- Published: 2004-09-20

**Particle Cluster Model Theory**

Overview:

Particle Cluster Model Theory explores the behavior of clusters of particles in various systems, including strongly correlated fermion systems, Janus fluids, and relativistic quantum mechanics. This theory has applications in condensed matter physics, statistical mechanics, and nuclear physics.

Relevant Authors, Research Papers, and Links:

- Bond-dependent slave-particle cluster theory based on density matrix expansion
- Authors: Zheting Jin, Sohrab Ismail-Beigi
- Link to Paper
- Download PDF
- Published: 2022-09-19

- A cluster-based mean-field and perturbative description of strongly correlated fermion systems. Application to the 1D and 2D Hubbard model
- Authors: Carlos A. Jiménez-Hoyos, Gustavo E. Scuseria
- Link to Paper
- Download PDF
- Published: 2015-05-21

- Particle-number projected Bogoliubov coupled cluster theory. Application to the pairing Hamiltonian
- Authors: Y. Qiu, T. M. Henderson, T. Duguet, G. E. Scuseria
- Link to Paper
- Download PDF
- Published: 2018-10-26

- Cluster theory of Janus particles
- Authors: Riccardo Fantoni, Achille Giacometti, Francesco Sciortino, Giorgio Pastore
- Link to Paper
- Download PDF
- Published: 2010-12-08

- Relativistic Quantum Mechanics – Particle Production and Cluster Properties
- Authors: W. N. Polyzou
- Link to Paper
- Download PDF
- Published: 2003-02-11

**Particle Pairing Theory**

Overview:

Particle Pairing Theory explores the pairing behavior of fermions and other particles in various systems, including nuclear physics, mesoscopic superconductors, and strongly correlated fermion systems. This theory has applications in understanding ground state correlations, collective behavior, and the transition between mean field and pairing dominated regimes.

Relevant Authors, Research Papers, and Links:

- Solving for the Particle-Number-Projected HFB Wavefunction
- Authors: L. Y. Jia
- Link to Paper
- Download PDF
- Published: 2015-01-15

- Treatment of like-particle pairing with quartets
- Authors: M. Sambataro, N. Sandulescu
- Link to Paper
- Download PDF
- Published: 2013-03-19

- A Number-Conserving Theory for Nuclear Pairing
- Authors: L. Y. Jia
- Link to Paper
- Download PDF
- Published: 2013-05-13

- The many levels pairing Hamiltonian for two pairs
- Authors: M. B. Barbaro, R. Cenni, A. Molinari, M. R. Quaglia
- Link to Paper
- Download PDF
- Published: 2003-06-23

- Density-matrix functionals for pairing in mesoscopic superconductors
- Authors: Denis Lacroix, Guillaume Hupin
- Link to Paper
- Download PDF
- Published: 2010-03-15

**Particle Transfer Reaction Theory**

Overview:

Particle Transfer Reaction Theory studies the transfer of particles between interacting systems, often within the context of nuclear reactions. This theory has applications in understanding nuclear dynamics, astrophysics, and the behavior of charged particles in various energy regimes.

Relevant Authors, Research Papers, and Links:

- Particle transfer reactions with the time-dependent Hartree-Fock theory using a particle number projection technique
- Authors: Cédric Simenel
- Link to Paper
- Download PDF
- Published: 2010-08-18

- Asymptotic theory of charged particle transfer reactions at low energies and nuclear astrophysics
- Authors: R. Yarmukhamedov, K. I. Tursunmakhatov, N. Burtebayev
- Link to Paper
- Download PDF
- Published: 2018-11-22

- Single-Particle Transfer and Nuclear Supersymmetry. Pick-Up and Stripping with SUSY
- Authors: J. Barea, R. Bijker, A. Frank, G. Loyola
- Link to Paper
- Download PDF
- Published: 2001-07-16

- Dispersion (asymptotic) theory of charged particle transfer reactions at low energies and nuclear astrophysics: I. the “non-dramatic” case
- Authors: R. Yarmukhamedov, K. I. Tursunmakhatov
- Link to Paper
- Download PDF
- Published: 2020-03-12

- Dispersion (asymptotic) theory of charged particle transfer reactions at low energies and nuclear astrophysics: II. the asymptotic normalization coefficients and their nuclear-astrophysical application
- Authors: R. Yarmukhamedov, K. I. Tursunmakhatov, N. Burtebayev
- Link to Paper
- Download PDF
- Published: 2020-03-12

**Particle Transmutation Theory**

Overview:

Particle Transmutation Theory explores the transformation of one type of particle into another, such as fermions transmuting into different flavors. This theory has applications in quantum mechanics, gauge theory, electromagnetic fields, and the understanding of fundamental particle interactions.

Relevant Authors, Research Papers, and Links:

- Fermion transmutation – a renormalization effect in gauge theory
- Authors: S. T. Tsou, H. M. Chan
- Link to Paper
- Download PDF
- Published: 2000-08-30

- Unifying Relations for Scattering Amplitudes
- Authors: Clifford Cheung, Chia-Hsien Shen, Congkao Wen
- Link to Paper
- Download PDF
- Published: 2017-05-08

- Engineering statistical transmutation of identical quantum particles
- Authors: Simone Barbarino, Rosario Fazio, Vlatko Vedral, Yuval Gefen
- Link to Paper
- Download PDF
- Published: 2018-06-21

- Transmutation of protons in a strong electromagnetic field
- Authors: Tobias N. Wistisen, Christoph H. Keitel, Antonino Di Piazza
- Link to Paper
- Download PDF
- Published: 2020-11-16

- Spin-statistics transmutation in relativistic quantum field theories of dyons
- Authors: K. Lechner, P. A. Marchetti
- Link to Paper
- Download PDF
- Published: 2000-10-31

**Particle Vibrational Energy Theory**

Overview:

Particle Vibrational Energy Theory explores the coupling between particles and vibrational modes within a system. This theory has applications in nuclear structure, quantum mechanics, and the understanding of single-particle dynamics influenced by collective vibrations.

Relevant Authors, Research Papers, and Links:

- Particle vibrational coupling in covariant density functional theory
- Authors: P. Ring, E. Litvinova
- Link to Paper
- Download PDF
- Published: 2009-09-07

- Particle-vibration coupling within covariant density functional theory
- Authors: E. Litvinova, P. Ring, V. Tselyaev
- Link to Paper
- Download PDF
- Published: 2007-05-08

- Beyond the mean field in the particle-vibration coupling scheme
- Authors: M. Baldo, P. F. Bortignon, G. Colo’, D. Rizzo, L. Sciacchitano
- Link to Paper
- Download PDF
- Published: 2015-07-09

- Covariant theory of particle-vibrational coupling and its effect on the single-particle spectrum
- Authors: E. Litvinova, P. Ring
- Link to Paper
- Download PDF
- Published: 2006-05-24

- Mean-Field Theory for Fermion Pairs and the ab initio Particle-Vibration-Coupling Approach
- Authors: Peter Schuck
- Link to Paper
- Download PDF
- Published: 2019-05-12

**Particle Wave Function Theory**

Overview:

Particle Wave Function Theory delves into the mathematical description of particles as wave functions. This theory is fundamental to quantum mechanics, exploring the probabilistic nature of particles, their interactions, and the relationship between particles and waves.

Relevant Authors, Research Papers, and Links:

- Wave function as geometric entity
- Authors: B. I. Lev
- Link to Paper
- Download PDF
- Published: 2011-02-10

- On Wave Function Representation of Particles as Shock Wave Discontinuities
- Authors: Babur M. Mirza
- Link to Paper
- Download PDF
- Published: 2015-05-31

- Free particle wavefunction in light of the minimum-length deformed quantum mechanics and some of its phenomenological implications
- Authors: Micheal S. Berger, Michael Maziashvili
- Link to Paper
- Download PDF
- Published: 2010-10-14

- The Wave Function and Quantum Reality
- Authors: Shan Gao
- Link to Paper
- Download PDF
- Published: 2011-08-04

- Two-particle wave function in four dimensional Ising model
- Authors: T. Yamazaki
- Link to Paper
- Download PDF
- Published: 2004-09-16

**Particle Weak Interaction Theory**

Overview:

Particle Weak Interaction Theory focuses on one of the four fundamental forces in nature, the weak force. This force is responsible for processes like beta decay in nuclear physics. The theory explores the interaction mechanisms, symmetry breaking, and the relationship with electroweak unification.

Relevant Authors, Research Papers, and Links:

- Lectures on the Theory of the Weak Interaction
- Authors: Michael E. Peskin
- Link to Paper
- Download PDF
- Published: 2017-08-29

- On the theory of interacting fields in Foldy-Wouthuysen representation
- Authors: V. P. Neznamov
- Link to Paper
- Download PDF
- Published: 2004-11-04

- Description of the weak interactions within the framework of electrodynamics
- Authors: D. L. Khokhlov
- Link to Paper
- Download PDF
- Published: 1998-09-19

- The Distinctive Feature of Weak Interactions and Some of Its Subsequences (Impossibility of Generation of Masses and Absence of the MSW Effect
- Authors: Kh. M. Beshtoev
- Link to Paper
- Download PDF
- Published: 2001-04-01

- Microscopic scattering theory for interacting bosons in weak random potentials
- Authors: Tobias Geiger, Andreas Buchleitner, Thomas Wellens
- Link to Paper
- Download PDF
- Published: 2013-07-18

Popular Theories:

The classic D-D fusion models propose that the observed effects are due to standard deuterium-deuterium (D-D) fusion occurring at low temperatures based on observation. However, more experiments demonstrate an observed phenomenon of transmutation of elements, excess heat, and production of small amounts of helium are observed in light water H_{2}O.

- Screening Potential Model: This model suggests that the Coulomb barrier between deuterium nuclei is reduced due to the presence of electrons in the metal lattice, allowing for fusion to occur at lower temperatures. The mathematical formulation for this model is based on the concept of screening potential, which is a function of the electron density in the metal lattice and the relative velocity of the deuterium nuclei.

- Hydrided Metal Lattice Model: This model proposes that the metal lattice in which the deuterium atoms are embedded plays a crucial role in facilitating fusion. The lattice may provide a mechanism for overcoming the Coulomb barrier, or it may alter the nuclear properties of the deuterium atoms in some way. The mathematical formulation for this model involves the calculation of the lattice energy and the interaction energy between the deuterium atoms and the lattice.

- Plasma Oscillation Model: This model suggests that fusion is facilitated by plasma oscillations within the metal lattice. These oscillations could potentially concentrate energy in a way that allows for fusion to occur. The mathematical formulation for this model involves the calculation of the plasma frequency and the energy transfer from the oscillations to the deuterium nuclei.

Non-nuclear models propose that the observed effects are not due to nuclear reactions at all, but rather to some other form of energy release. There are several variations of this model discussed in the paper:

- Chemical Reaction Model: This model suggests that the observed heat is due to chemical reactions within the metal lattice. The mathematical formulation for this model involves the calculation of the reaction rate and the heat of reaction for the proposed chemical reactions.

- Mechanical Energy Model: This model proposes that the observed heat is due to the release of mechanical energy, such as the energy stored in defects in the metal lattice. The mathematical formulation for this model involves the calculation of the energy stored in the lattice defects and the rate at which this energy is released.

- Electromagnetic Energy Model: This model suggests that the observed heat is due to the release of electromagnetic energy. The mathematical formulation for this model involves the calculation of the electromagnetic field strength and the rate at which energy is released from the field.

Now we will examine some of the more popular theoretical models of LENR/LANR and see if there are any similarities between the different theories. We will analyze and visualize the theoretical models of Low Energy Nuclear Reactions (LENR), Lattice Assisted Nuclear Reactions (LANR), and Lattice Confinement Fusion (LCF).

The models we will explore include:

- Classic D-D Fusion Models
- Screening Potential Model
- Hydrided Metal Lattice Model
- Plasma Oscillation Model
- Chemical Reaction Model,Mechanical Energy Model,Electromagnetic Energy Model
- Widom-Larsen Theory
- Holmlid Theory
- Hagelstein Theory
- Storms Theory
- Takahashi’s Tetrahedral Symmetric Condensate (TSC) Theory

We will begin by summarizing each model and then proceed to visualize the key components and interactions within these models.

Let’s dive into the detailed aspects of the theoretical models for Low Energy Nuclear Reactions (LENR), Lattice Assisted Nuclear Reactions (LANR), and Lattice Confinement Fusion (LCF) from our training datasets. These models provide insights into the underlying mechanisms that may be responsible for the observed phenomena in LENR/LANR/LCF experiments.

**1. Classic D-D Fusion Models**

The classic D-D fusion models propose that the observed effects are due to standard deuterium-deuterium (D-D) fusion occurring at low temperatures. This is based on the observation of phenomena such as transmutation of elements, excess heat, and production of small amounts of helium in light water H2O.

**2. Screening Potential Model**

This model suggests that the Coulomb barrier between deuterium nuclei is reduced due to the presence of electrons in the metal lattice. This allows for fusion to occur at lower temperatures. The mathematical formulation for this model is based on the concept of screening potential, a function of the electron density in the metal lattice and the relative velocity of the deuterium nuclei.

**3. Hydrided Metal Lattice Model**

This model proposes that the metal lattice in which the deuterium atoms are embedded plays a crucial role in facilitating fusion. The lattice may provide a mechanism for overcoming the Coulomb barrier, or it may alter the nuclear properties of the deuterium atoms. The mathematical formulation involves the calculation of the lattice energy and the interaction energy between the deuterium atoms and the lattice.

**4. Plasma Oscillation Model**

This model suggests that fusion is facilitated by plasma oscillations within the metal lattice. These oscillations could potentially concentrate energy in a way that allows for fusion to occur. The mathematical formulation involves the calculation of the plasma frequency and the energy transfer from the oscillations to the deuterium nuclei.

**5. Non-nuclear Models**

These models propose that the observed effects are not due to nuclear reactions but rather to some other form of energy release. Variations include:

- Chemical Reaction Model: The observed heat is due to chemical reactions within the metal lattice.
- Mechanical Energy Model: The observed heat is due to the release of mechanical energy, such as the energy stored in defects in the metal lattice.
- Electromagnetic Energy Model: The observed heat is due to the release of electromagnetic energy.

**6. Widom-Larsen Theory**

This theory proposes that LENR occurs through the creation of ultra-low-momentum neutrons that can be absorbed by nuclei, leading to the formation of heavier elements. Key aspects include the creation of heavy electrons, ultra-low-momentum (ULM) neutrons, capture of ULM neutrons, and beta decay creation of new elements and isotopes.

**7. Holmlid Theory**

This theory suggests that LENR can be explained by the formation of ultra-dense hydrogen clusters with Spin-Based Rydberg Matter that can undergo nuclear fusion at low temperatures. Key aspects include ultra-dense hydrogen and deuterium, kinetic energy release, spin-based quantum material, and Rydberg matter structure.

**8. Hagelstein Theory**

This theory proposes that LENR can occur through the creation of coherent excitations in the lattice structure of metals, leading to the formation of nuclear active sites. Key aspects include relativistic interaction, up-conversion of vibrational quanta, disintegration as a coherent quantum process, and selective disintegration.

**9. Storms Theory**

This theory suggests that LENR can be explained by a Hydroton model. Key aspects include condensed matter formation, neutron chain reactions, photon excitation and emissions, and reaction longevity.

**10. Takahashi’s Tetrahedral Symmetric Condensate (TSC) Theory**

This theory involves the formation of a tetrahedral symmetric condensate (TSC) of four deuterium or hydrogen atoms in a metal lattice. Key aspects include the formation of TSC, Bose-Einstein condensation, types of fusion, and energy release.

These theoretical models provide diverse perspectives on the underlying mechanisms of LENR/LANR/LCF. Understanding these models is essential for advancing research and development in this field.

Theoretical Analysis using machine learning:

The Venn diagram below illustrates the commonalities and differences among various theoretical models of Low Energy Nuclear Reactions (LENR). The diagram is divided into three main circles, each representing a key aspect shared by some of the theories.

**Fusion at Low Temperatures**

This circle includes theories that propose fusion occurring at low temperatures. Theories such as Classic D-D Fusion Models fall into this category.

**Involvement of Metal Lattice**

This circle encompasses theories that emphasize the role of the metal lattice in facilitating fusion. Models like the Hydrided Metal Lattice Model and the Plasma Oscillation Model are examples.

**Excess Heat Production**

This circle represents theories that explain the observed excess heat in LENR experiments. The Screening Potential Model is an example of this.

**Intersections**

The intersections between these circles represent additional commonalities between the 10 theoretical models identified above:

- Formation of New Elements or Isotopes: Some theories propose the creation of new elements or isotopes.
- Complex Interactions: This includes theories that involve complex interactions within the system, such as the Hagelstein Theory.
- Alternative Energy Release Mechanisms: This includes non-nuclear models that propose alternative mechanisms for energy release, such as chemical, mechanical, or electromagnetic energy.

This visualization was created by GPT-4 to help in understanding the overlapping aspects of the different theoretical models, highlighting the multifaceted nature of LENR. It also shows that while there are unique aspects to each theory, there are underlying themes that many of them share, such as the involvement of metal lattice and the production of excess heat.

LENR Simulations and Predictive Modeling:

With the use of Python, GPT4, and a coding environment like VS Code, we were able to develop a simple simulation based upon some known physical laws and their mathematical descriptions.

Mathematical Constants for Simulation purposes:

Python Script of 2D Lattice Catalyzed Fusion Simulation:

##2d LCF model v2##

#import libraries

import numpy as np

import matplotlib.pyplot as plt

from scipy.ndimage import gaussian_filter

from matplotlib.animation import FuncAnimation

# Define the size of the grid

grid_size = (100, 100)

# Create a 2D array for each physical quantity

density = np.zeros(grid_size) # Hydrogen density

pressure = np.zeros(grid_size) # Pressure

velocity_x = np.zeros(grid_size) # Velocity x-component

velocity_y = np.zeros(grid_size) # Velocity y-component

magnetic_field_x = np.zeros(grid_size) # Magnetic field x-component

magnetic_field_y = np.zeros(grid_size) # Magnetic field y-component

material_properties = np.zeros(grid_size) # Material properties placeholder

environment_coupling = np.zeros(grid_size) # Environment coupling placeholder

stochastic_effects = np.random.rand(*grid_size) # Stochastic effects placeholder

# Initialize hydrogen concentration with a higher concentration at specific sites

density.fill(0.5)

density[45:55, 45:55] = 1 # Higher concentration in the center

# Initialize local electric fields (due to lattice imperfections)

electric_field = np.random.rand(*grid_size)

# Initialize electromagnetic field (for coherent motion)

em_field = np.random.rand(*grid_size) # Initialize with a random field

# Placeholder parameters

atomic_spacing = 0.1 # nanometers

energy_density_required = 1e6 # J/m^3

def check_fusion_conditions(site):

# Placeholder for fusion condition check

E = electric_field[site]

H_concentration = density[site]

lattice_defect = 0 # Placeholder for lattice defect

EM = em_field[site]

material_property = material_properties[site]

environment_effect = environment_coupling[site]

stochastic_effect = stochastic_effects[site]

# Placeholder for fusion conditions

fusion_conditions = E > 0.5 and H_concentration > 0.5 and EM > 0.5 and material_property > 0.5 and environment_effect > 0.5 and stochastic_effect > 0.5

return fusion_conditions

def lenr_event(site):

# Placeholder for LENR event simulation

pressure[site] += 1

density[site] -= 0.1

def update_lattice():

# Update the lattice based on interactions and energy equations

global density, em_field

for i in range(grid_size[0]):

for j in range(grid_size[1]):

site = (i, j)

if check_fusion_conditions(site):

lenr_event(site)

# Simulate diffusion of hydrogen

density = gaussian_filter(density, sigma=1)

# Add some dynamics to the electromagnetic field

em_field = np.roll(em_field, shift=1, axis=0) # Shifts the field one step

def animate(i):

update_lattice()

ax[0].imshow(density, cmap=’hot’, interpolation=’none’)

ax[0].set_title(‘Hydrogen Concentration on Lattice’)

ax[0].set_xlabel(f’Lattice Site (Atomic Spacing = {atomic_spacing} nm)’)

ax[0].set_ylabel(f’Lattice Site (Atomic Spacing = {atomic_spacing} nm)’)

ax[1].imshow(em_field, cmap=’viridis’, interpolation=’none’)

ax[1].set_title(‘Electromagnetic Field on Lattice’)

ax[1].set_xlabel(f’Lattice Site (Atomic Spacing = {atomic_spacing} nm)’)

ax[1].set_ylabel(f’Lattice Site (Atomic Spacing = {atomic_spacing} nm)’)

fig.suptitle(f’Time step: {i+1}’)

fig, ax = plt.subplots(1, 2, figsize=(10, 5))

ani = FuncAnimation(fig, animate, frames=10) # Reduced frames for demonstration purposes

plt.show()

# Define Constants and Experimental variables:

#k_B = 1.380649e-23 # Boltzmann constant

#hbar = 1.0545718e-34 # Reduced Planck constant

#e = 1.60217662e-19 # Elementary charge

#m_p = 1.6726219e-27 # Proton mass

#m_n = 1.674929e-27 # Neutron mass

#Mathematical Formulas of Constants:

# k_B = 1.380649 × 10⁻²³ J K⁻¹ (Boltzmann constant)

# ħ = 1.0545718 × 10⁻³⁴ J s (Reduced Planck constant)

# e = 1.60217662 × 10⁻¹⁹ C (Elementary charge)

# m_p = 1.6726219 × 10⁻²⁷ kg (Proton mass)

# m_n = 1.674929 × 10⁻²⁷ kg (Neutron mass)

# Define Material properties

#Palladium = {‘Z’: 46, ‘A’: 106.42, ‘Density’: 12.023g/cm³, ‘melting_point’: 1828.05K(1554.9 °C), ‘boiling_point’: 3236K (2963 °C), Crystal: face-centered cubic (fcc)}

#Nickel = {‘Z’: 28, ‘A’: 58.6934, ‘Density’: 8.908g/cm³, ‘melting_point’: 1728K (1455 °C), ‘boiling_point’: 3186K (2913 °C), Crystal: face-centered cubic (fcc)}

#Platinum = {‘Z’: 78, ‘A’: 195.084, ‘Density’: 21.45g/cm³, ‘melting_point’: 2041.4K (1768.3 °C), ‘boiling_point’: 4098K (3825 °C), Crystal: face-centered cubic (fcc)}

#Titanium = {‘Z’: 22, ‘A’: 47.867, ‘Density’: 4.506g/cm³, ‘melting_point’: 1941K (1668 °C), ‘boiling_point’: 3560K (3287 °C), Crystal: hexagonal close-packed (hcp)}

#Tungsten = {‘Z’: 74, ‘A’: 183.84, ‘Density’: 19.25g/cm³, ‘melting_point’: 3695K (3422 °C), ‘boiling_point’: 6203K (5930 °C), Crystal: body-centered cubic (bcc)}

#Zirconium = {‘Z’: 40, ‘A’: 91.224, ‘Density’: 6.506g/cm³, ‘melting_point’: 2128K (1855 °C), ‘boiling_point’: 4682K (4409 °C), Crystal: hexagonal close-packed (hcp)}

# Define function to calculate fusion rate

#def fusion_rate(T, n):

# Calculate cross section

#sigma = 1e-24 * (e ** 2 / (4 * np.pi * hbar * c)) ** 2 / (k_B * T) ** 2 * np.exp(-3 * np.pi / (4 * np.sqrt(2)) * (Z_1 * Z_2 * e ** 2 / (hbar * c)) ** 2 / (k_B * T))

# Calculate fusion rate

#rate = n_1 * n_2 * sigma * v_rel

#return rate

# Define function to simulate LENR

#def simulate_lenr(T, n):

# Calculate fusion rate

#rate = fusion_rate(T, n)

# Calculate time to fusion

#time_to_fusion = 1 / rate

#return time_to_fusion

# Test hypothesis

#T = 300 # Temperature in Kelvin

#n = 1e28 # Density of hydrogen atoms in m^-3

#time_to_fusion = simulate_lenr(T, n)

#if time_to_fusion < 1e-9:

#print(‘LENR occurred!’)

#else:

#print(‘LENR did not occur.’)

Python Script of 2D Lattice Catalyzed Fusion Simulation

Asymmetrical Electrodes MHD Simulations

The Importance of Open Source vs Closed Source technology:

We also wanted to gather and compare the data of development in technological advancement for both Computer Science (Machine Learning) and LENR, to see why one would develop faster than the other.

We gathered statistical data of the adoption rates of Open Source compared to Closed source technologies to see if the rate of innovation increased or decreased in 3 particular fields of interest. This was to assess if LENR would have more mainstream adoption through Open Source or Closed Source Practices and do a brief examination of how Intellectual Property affects technological adoption rates.

LLM Open vs Closed Source:https://abiaryan.com/posts/intro-llms/

Open-source LLMs:

1. Accessibility: Open-source models are generally available for anyone to download, modify, and use. This democratizes access to cutting-edge technology.

2. Community Contribution: Open-source projects often benefit from a large community of developers and researchers who contribute to improving the model, fixing bugs, and extending functionalities.

3. Transparency: The algorithms and training data are open for scrutiny, which is crucial for understanding model behavior, biases, and vulnerabilities.

4. Cost: Usually free to use, which lowers the barrier to entry for startups and individual developers.

5. Innovation: Open-source models often serve as the foundation for a wide range of applications and new research, accelerating the pace of innovation.

6. Trust: Open inspection of the code can lead to higher trust, especially in sensitive applications like healthcare or legal decision-making.

Closed-source LLMs:

1. Control: The company or entity that owns the model has full control over its usage, often requiring users to pay for API access.

2. Quality Assurance*: With a dedicated team and resources, closed-source models may offer better quality assurance and customer support.

3. Business Model: Easier to monetize as the code is proprietary.

4. Data Security: In some cases, closed-source models may offer better data security as the internal workings are not exposed.

5. Limited Scrutiny: The lack of transparency makes it difficult to scrutinize the model for biases or vulnerabilities.

Importance of Open-source:

1. Accelerated Learning and Research: Open-source models are accessible to researchers worldwide, which speeds up machine learning and AI research.

2. Collaborative Effort: The open-source nature invites a collaborative approach, pooling the collective intelligence of developers and researchers globally.

3. Ethical and Fair AI: Open-source allows for the community to identify and work on fixing biases in AI models, making them more ethical and fair over time.

4. Lower Costs: For businesses and individual developers, the absence of licensing fees can make development cheaper and faster.

Given the ratio of 10:3:4 (open-source: partially open-source: closed-source) in our small dataset from 2021, it’s evident that the AI community is leaning towards open-source. This could be a significant factor in their popularity, as they align well with academic research needs, allow for broad-based innovation, and offer a level of transparency and scrutiny that is becoming increasingly important in AI ethics.

Software Examples:

-Open Source Software

1. A survey found that 89% of businesses run open-source software internally, while 65% contribute to open-source software projects ([source](https://www.zdnet.com/article/open-source-is-everywhere-in-business-heres-whats-driving-adoption/)).

2. A 2008 report by the Standish Group stated that adoption of open-source software models has resulted in savings of about $60 billion per year for consumers ([source](https://en.wikipedia.org/wiki/Open-source_software)).

3. As per a study titled “Future of Open Source” ~90 percent of firms agreed that Open Source offers room for innovation, enhance productivity and ([source](https://teknospire.com/open-source-software-adoption-initiatives-value-proposition-risks-impact/)).

-Closed Source Software

1. The search results for closed source software adoption rates are not as straightforward as those for open by their very nature compared to open source software. However, it’s clear that closed source software has had a significant presence in the market, particularly in the era before the rise of open source ([source](https://www.channelfutures.com/open-source/a-brief-history-of-free-and-open-source-software-licensing)).

2. Some sources suggest that non-open source software is too fragile and risky for modern application development ([source](https://blog.tidelift.com/the-closed-source-sustainability-crisis)).

Hardware Examples:

-Open Source Hardware

1. Open Source Hardware financial market is estimated to reach $2365.4 Million by 2026; growing at a CAGR of 8.4% till 2026 ([source](https://bizlytik.com/report/open-source-hardware-market/)).

2. Combining both Arduino and 3-D printing the savings averaged 94% for free and open source tools over commercial equivalents ([source](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7480774/)).

-Closed Source Hardware

1. The search results for closed source hardware adoption rates are not as clear as those for open source hardware. However, it’s suggested that specialized hardware might be able to offset significant development costs and build a community of eager adopters ([source](https://deploy.equinix.com/blog/specialized-hardware-and-open-source/)).

Pros and Cons of Open Source vs. Closed Source in Science & Technology:

We examined the pros and cons of Open vs Closed Source Science and Technology using GPT4 and have come to the following results.

-Open Source

Pros:

1. Collaboration: Enables researchers and developers to collaborate across disciplines and countries.

2. Transparency: Code and methods are publicly available, making it easier to identify errors or biases.

3. Cost-Effective: Generally free to use, allowing for greater accessibility, especially for smaller labs or startups.

4. Accelerated Innovation: Anyone can contribute, leading to faster development and the incorporation of the best ideas.

5. Reproducibility: Easier for other scientists to reproduce experiments and verify results.

Cons:

1. Quality Variability: Open-source projects may lack the polish or support of commercial software.

2. Security Risks: Open nature may expose vulnerabilities, although these often get quickly patched.

3. Initial Complexity: May have a steeper learning curve due to lack of dedicated customer support.

4. Funding: Sustaining large open-source projects can be financially challenging without a consistent funding model.

5. Fragmentation: Multiple versions or forks can create confusion and dilute community focus.

-Closed Source

Pros:

1. Quality Assurance: Often backed by companies offering support and consistent updates.

2. User-Friendly: Generally easier to use, with better documentation and user interfaces.

3. Security: Source code is not exposed, providing some level of inherent security.

4. Funding: Commercial model ensures a stream of funding for ongoing development.

5. Standardization: Proprietary software often sets industry standards due to widespread adoption.

Cons:

1. High Cost: Licensing fees can be prohibitive for smaller organizations or individual researchers.

2. Limited Customization: Users can’t modify the software to fit their specific needs.

3. Vendor Lock-in: Users are dependent on a single vendor for updates and support.

4. Transparency: Lack of transparency can hinder scientific verification and peer review.

5. Collaboration: Proprietary nature can limit collaborative efforts and the sharing of knowledge.

These findings suggest that open source software and hardware have been widely adopted and have provided significant cost savings with public accessibility. However, the adoption rates of closed source software and hardware are not as clearly documented by their nature. In the context of LENR/LANR research, it’s possible that the openness of the research (i.e., whether it’s conducted in an open source manner or not) could influence the progress of the research.

It’s important to note that more specific research and development would be needed to confirm this economic hypothesis.

Conclusion: The use of machine learning techniques to analyze the data from LENR experiments has the potential to provide valuable insights into the underlying mechanisms of LENR. This research represents a novel approach to the study of LENR and has the potential to significantly advance our understanding of this fascinating phenomenon. Keeping an open and transparent community for LENR will likely accelerate it’s development as more are able to contribute to the greater body of knowledge.

The findings of the research contribute to an improved understanding of LENR and LANR, suggest potential new directions for future research, and demonstrate the potential of machine learning techniques for analyzing complex data sets and extracting meaningful insights. The visualizations created as part of the research, including 3D representations of the mathematics involved in LENR and LANR, helped to better understand and communicate the complex mathematical concepts involved in these phenomena.

The research also contributes to the field of machine learning by demonstrating the potential of these techniques for analyzing complex data sets and extracting meaningful insights. This could inspire further applications of machine learning techniques in other fields of research.

In conclusion, this research represents a significant step forward in the investigation of LENR and LANR using machine learning techniques. It provides a foundation for future research in this field and demonstrates the potential of machine learning techniques for advancing our understanding of complex phenomena.

Acknowledgements: We would like to acknowledge the contributions of the researchers who have conducted experiments and developed theories in both fusion and machine learning. Their work has been vital in helping to advance the field of Fusion energy and Machine Learning. We would also like to thank the LENR Forum and other online communities for their support and collaboration. A special thanks to the LENR-Forum Team and Jed Rothwell with LENR-CANR.org. Without his organization’s well documented catalog, this research would have not been possible.

Data sets and python scripts can be found at https://huggingface.co/ConsciousEnergies and https://github.com/ConsciousEnergy/UMLENR

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