Phonon Assisted Fusion

This paper continues and expands upon a paper presented at ICCF-22 related to phonon assisted fusion.

The overall thesis is that there exist sparsely occupied “nearly free” deuteron states which are modelled similarly to nearly free electrons in traditional solid state physics. These states are occupied in the range of 10-4 , depending on D doping and lattice temperature.

The probability amplitude of the states is largest in regions other than where Pd and bound are. The charge of nearly free D’s, whose spatial extent is in the range of .4 Angstroms, is neutralized by a much shorter electron Debye length than the local de Broglie wavelength, so D-D repulsion is negligible, and nearly free D’s overlap.

This results in a “large” excited compound (roughly .4Angstrom) nucleus that could decay either through the normal paths, with hot particles, or through an additional path, which involves multiphonon assisted transitions. The transition rates for the traditional paths can be shown to be decreased by ~28 orders of magnitude because of the increased volume of the compound nucleus, whereas the phonon assisted rates are appreciable under certain conditions.

When threshold conditions are right for a specific phonon mode, the mode becomes rapidly occupied, with the created phonons draining energy from the excited nucleus. The mode occupation grows until a saturation point is reached where the mode decay rate, which is phonon occupation dependent, exceeds the phonon generation rate.

Hence, the total power released depends on the number of modes above threshold, and the number of phonons in those modes, as limited by saturation. This leads to two formulas: one for mode threshold, and a second for mode occupation/power generation, which are derived.

The threshold equation and the power equation depend on parameters which are spatially non-uniform, temperature and pressure dependent, and generally not measured locally, if at all. This leads to huge nonuniformities and experiment-to-experiment variations.

The equations give clues as to how to choose and improve LENR systems, including hydrogen systems.

• The impact of pressure, impurities and vacancies on phonon densities of states at a given wavevector, and the consequent impact on thresholds

• The impact of external stimulation of phonon mode occupation to initiate a reaction

• The number of “nearly free deuterons” as a function of temperature, doping, externally applied potentials

• The material lattice parameter The phonon decay rate as a function of k and mode occupancy, temperature, stress and host lattice

Newly available information on phonon spectra in nearly pure Pd:D, and stressed Pd:D suggest that phonon lifetimes are strongly influenced in perhaps unappreciated ways.

The Cold Fusion/LENR Ping List

http://www.freerepublic.com/tag/coldfusion/index?tab=articles

Keywords: ColdFusion; LENR; lanr; CMNS
chat—science

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http://lenr-canr.org/

Vortex-L
http://tinyurl.com/pxtqx3y

Acronyms:
LENR: Low Energy Nuclear Reactions. [Also Lattice Enabled Nuclear Reactions, but seldom used]
CANR: Chemical Assisted Nuclear Reactions [fallen into disuse along with LANR/Lattice Assisted Nuclear Reactions]
CMNS: Condensed Matter Nuclear Science
LCF: Lattice Confined Fusion [NASA’s term for it]

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

https://www.abebooks.com/9780967854809/Excess-Heat-Why-Cold-Fusion-0967854806/plp

Updated No Internal Trolling Rules for FR per Jim Robinson

https://freerepublic.com/focus/f-news/3928396/posts

If someone says stop, then stop. Do not enter onto a thread on a topic you don’t like just to disrupt, rattle cages, poke sticks, insult the regulars, or engage in trolling activities, etc. ~Jim Robinson

The issue isn’t whether we allow skepticism, it is whether we allow hyperskeptics and skeptopaths to ruin the scientific dialog. Such FReepers who persist in polluting these threads have been asked to leave, and we are asking that they open their own threads if they have comments.

https://freerepublic.com/focus/chat/3977426/posts?page=19#19

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This topic has a following, people who wish to learn and discuss the materials presented.

Please refrain from posting anything that doesn’t legitimately address the issue.

Something is going on in this segment of science. There are a considerable number of research groups studying the matter.

19 posted on 7/19/2021, 6:45:09 PM by Sidebar Moderator

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This is a followup to his ICCF-22 article on PHonon Assisted Fusion.

  


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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