HD/He-3 phonon-nuclear coupling matrix element

We have recently worked on the calculation of the phonon-nuclear coupling matrix element for the HD/He-3 transition. This matrix element is important in connection with excess heat in light water reactions, as well as low-energy nuclear emission in experiments with hydrogen (and some deuterium).

It is also one of the simplest to analyze with nuclear models. We have developed a reduction of the relativistic boost interaction for the lowest order meson exchange potential based on pseudoscalar and pseudovector interactions. The pseudoscalar interaction does not contribute, and we find a complicated but useful expression in the pseudovector case.

We have carried out a reduction based on the old Gerjuoy-Schwinger approach to wave function construction. This has advantages in terms of allowing for Mathematica to reduce the spin and isospin algebra, resulting in equations fully symmetric in particle coordinates. This makes things easier to evaluate numerically.

We have developed explicit expressions for the lowest-order boosted central and tensor potential interactions, which are readily evaluated to get numerical estimates. Having a solid number for this phonon-nuclear coupling matrix element is by itself useful.

However, an unexpected consequence of the analysis is that we may be able to say something important about the state of the HD molecule in the lattice if it is to have the strongest phonon-nuclear interaction -- that is we need a P-state rotational admixture.

There has been no agreement as to how excess heat is produced in the Fleischmann-Pons experiment over the past three decades. We have pursued ideas and models that relate to the interaction between nuclei and vibrations in the lattice, making progress step by step.

During the past year some of the problems which have stood in the way have found solutions. We now have a picture that looks to address most if not all of the important issues.

The strongest interaction between nuclei and vibrations appears to come about due to the relativistic boost correction of the nuclear interaction for nuclei vibrating in a lattice. We have made progress in developing quantitative estimates for this interaction in some specific cases, and work is ongoing to calculate additional examples.

The transfer of excitation from one nucleus to another provides the basic engine within the theory for many anomalies. Excitation transfer due to direct nucleus-nucleus interaction is possible, but weak.

A much stronger interaction is possible when many nuclei interact with a highly excited uniform THz vibrational model. Excitation transfer and more sophisticated interactions are hindered by destructive interference in basic models.

In previous years we relied on loss effects asymmetric off of resonance to break the destructive interference. Last year we found that this effect was insufficient to account for excitation transfer results in our lab, which meant that something else even bigger was happening.

It seems clear at this point that the shift of nuclear levels off of resonance lies at the heart of the enhancements. Models including this effect appear capable of connecting quantitatively with experiment. Off-resonant energy shifts of nuclear levels is expected to similarly eliminate much of the destructive interference associated with massive up-conversion and down-conversion needed for excess heat production, and for collimated x-ray emission within the models.

We also consider the connection between ongoing excitation transfer experiments and ion beam experiments in our lab to the models under development.

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Best book to get started on this subject:
EXCESS HEAT
Why Cold Fusion Research Prevailed by Charles Beaudette

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https://iscmns.org/blog/wp-content/uploads/2019/09/Abstracts.pdf

S Dana Seccombe: Phonon Assisted Nuclear Fusion Mode
The paper presents a theoretical model for phonon assisted nuclear fusion. Though initially developed
around experimental results in the Pd:D system, the results are applicable to the Ni: H system by changing model
parameters.
The thesis of the paper is that the presence of phonons in the lattice provides an additional channel not
present in plasma phase nuclear interactions. Using the model, one can compute a fusion threshold as a function
of crystal size, temperature, and D doping,-—and phonon spectra and lifetime-— which is itself a function or
crystal doping , defect density, shape, orientation.
The theory doesn’t require the postulation of exotic particles or new physics; it uses only previously wellknown principles of solid state physics which has described multiphonon non-radiative transfers in phosphors;
and a simple coupling mechanism between phonons and D-D wavefunctions.
The model starts with Fermi’s Golden rule as further developed by Heitler for multi-state virtual transitions
(here,>109
phonons) and quantitatively predicts a D-D transition rate to the He ground state as a function of
known parameters. At the same time, calculation of Fermi’s hfi for traditional branching paths (to tritium or
helium 3, or He4+gamma’s) with near atomic sized D wave functions (deBroglie wavelengths) show those
transitions will have low probability.
The model uses D probability amplitudes between lattice sites, and calculates the change in nuclear energy of
overlapping D’s as a function of optical phonon mode occupation. Though extremely small, these changes are the
hfi in Heitlers multi state/multichannel rate calculations. Though there are >109
sequential transitions (tending to
dramatically lower rates), this is compensated for by the approximately (2 d)
levels parallel paths, where d is the
number of degrees of freedom in a small crystal (say 1012) and levels is the number of phonons (say >109
). Those
calculations show that, once a certain threshold is reached in a combination of crystal size, doping, and presence
of coherent optical phonons, additional phonons are rapidly created, initiating a run-away situation in the crystal
similar to that found in lasers above threshold. In both cases, the actual reaction then is limited by the availability
of reactants, not the Golden Rule transition rate. [It is shown that Pd:D, in a “NaCl like” crystal lattice has a very
narrow longitudinal optical spectrum that leads to coherency and long lifetimes.] The subsequent reaction will be
steady state (life after death) if the reactants continue to diffuse into the reaction region at a rate high enough to
sustain the necessary optical phonon population, whose size is dependent on the optical phonon lifetime. That
lifetime is inherently longer in perfect PdD crystals (or crystals near stoichiometry and nearly defect free). If not,
episodic reactions occur when a threshold condition occurs, then local reactants are again depleted in a
relaxation phenomenon.
Any artificial means to create a larger population of optical phonons (electrical excitation of optical phonons,
directly for example; or through plasmons) will tend to initiate fusion, given other factors are within a range that,
combined with the phonon contribution result in exceeding threshold.
The model predicts/explains the following often observed effects:
 Why He with heat is by far the dominant pathway in Pd:D
 Why there is great variability in the success of experiments, including apparent “nuclear active entities”
 When and why “life after death” occurs
 Why there are “explosive” local reactions, and how they can be mitigated or controlled
 Why Ni:H and Pd:D reactions can occur
 Why Raman anti-Stokes lines are correlated with excess heat
Understanding of the phenomena via the model allows one to predict leverage areas for design of energy
producing systems, and tools for materials control and analysis (for example, optical phonon lifetime and
coherence as a function of material/process parameters and spatial inhomogeneity). Conversely, correlation of
optical phonon lifetime and coherence (and other model parameters) allow a check on the model itself.

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