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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.