Historical research guide · 0782 · 2022
Recent Progress on Phonon-Nuclear Theoretical Models
Peter L. Hagelstein
In one minute
Peter Hagelstein, at MIT, has spent three decades on one question about the Fleischmann–Pons experiment: if the heat is nuclear, where are the fast particles? Textbook nuclear reactions throw their energy out as flying fragments, and those are not seen in amounts that match the heat measured. His answer is that the energy leaves as lattice vibration instead of as debris, and this review is the working state of the model built to make that happen. The chain has three links. A 24 MeV quantum, from a deuterium pair becoming helium, is handed to a nucleus in the metal. That excitation is then subdivided across more and more nuclei at lower and lower energy. What is left is down-converted into an enormous number of vibrational quanta. The coupling that allows any of it is a relativistic phonon–nuclear interaction Hagelstein derives from a many-nucleon Dirac treatment, and the prize he points to is a change in the rate law itself, from the square of the tunnelling factor to the tunnelling factor alone.
Connection
Chapter 12 is about making nuclei react inside a lattice rather than inside a plasma, and this is the most developed account of how the released energy could arrive as heat with no commensurate flying particles. Its rate argument is the one to carry away: coherence changes the exponent on the tunnelling factor, and that exponent is the whole difference between a rate nobody could measure and a rate that runs a device.
From the source
The theoretical starting point is the absence of commensurate energetic nuclear particles, which implies that nature has found a way to take a very large 24 MeV nuclear quantum and split it into an enormous number of lower energy quanta — on the order of a billion of them — a down-conversion with no precedent in the literature.Section 1, Introduction
Coherence changes the rate law. An incoherent fusion rate is governed by the Golden Rule and is quadratic in the coupling matrix element, so it carries the Gamow tunnelling factor squared; a coherent quantum process can be linear in that matrix element and therefore linear in the Gamow factor alone. Since the Gamow factor here is of order ten to the minus fortieth power, the difference is a dramatic acceleration of the reaction rate.Section 1, Introduction, the paragraph accompanying Figure 1
The coupling proposed is relativistic rather than electromagnetic: a nucleus embedded in a lattice must be consistent with relativity, undergoing Lorentz contraction and spin and isospin rearrangement as it moves, so changes in the internal nuclear state as the nucleus moves with the lattice vibrations imply a low-order phonon-nuclear interaction stronger than the weak second-order interaction available through local electric and magnetic fields — and it answers how fermi-scale internal nuclear degrees of freedom can talk to vibrations organised across a great many atoms.Section 1, Introduction; Section 2, lowest-order phonon-nuclear interaction from the Dirac model; Section 6, covariant model
The excess heat model runs in three stages: excitation transfer of the 24 MeV quantum from the deuterium-to-helium transition into a palladium or other lattice nucleus; a subdivision step giving two excited nuclei at roughly 12 MeV each, and further steps reaching thousands of nuclei at much lower excitation, likely impurity nuclei since the palladium isotopes have no long-lived low-lying excited states; and finally down-conversion of that lower nuclear excitation into phonons.Section 1, Figure 1; Section 13, Subdivision; Section 16, Figure 18
There is hardware behind the theory. Hagelstein’s laboratory reports evidence for resonant phonon-mediated nuclear excitation in observations of dynamic angular anisotropy, and observations consistent with non-resonant excitation transfer in delocalization experiments, using cobalt-57 decaying into excited iron-57 under stress-induced terahertz vibration; because the location, frequency and strength of those vibrations are not known well enough to model, a simpler resonant excitation transfer experiment in a near single crystal sample is set out, choosing a nucleus with an electric dipole transition so that only one phonon need be exchanged per nuclear transition.Section 1, Introduction; Section 14, Phase coherence with resonant excitation transfer, and Sections 14.1 and 14.2
A caesium-137 excited state at 5494.2 keV is identified as nearly resonant with the hydrogen-deuterium to helium-3 transition at 5493.478 keV, which suggests a route by which repeated excitation transfer could populate highly excited caesium-137 states that beta decay faster than the ground state — a possible mechanism behind the accelerated decay rates reported by Kornilova, Vysotskii and coworkers, and a test that would be run by measuring the 661 keV emission before and after.Sections 10.2 and 11, with Figures 8 and 9; Section 11.4, caesium-137 as an indicator of anomalous energy exchange
The way in
https://doi.org/10.70923/001c.72598How to cite it
Peter L. Hagelstein (2022) Recent Progress on Phonon-Nuclear Theoretical Models doi:10.70923/001c.72598