Coherent Oscillations of Protons in Hydrogen-Loaded Metals

We review recent calculations and numerical simulations showing the formation of coherent states of protons in hydrogen-loaded metals with a cubic crystal lattice. The characteristic frequencies discussed here are the local proton frequency, the plasma frequency, and the resonant confined electromagnetic frequency; depending on the adopted parameters, they are of order 1013–1014Hz. They are far from the much higher frequency corresponding to the full electron-capture energy transfer. In these states protons oscillate coherently and in a fixed phase relation with a strong high-frequency electric field which is trapped in the material, especially if the material is made of micro-powders. The energy gap of the coherent ground state is estimated to be well above thermal energies, of the order of a fraction of an eV per particle, and therefore large enough to make the state robust against thermal fluctuations. The analytical calculations address the realistic case of a large number of protons, in the rotating-wave approximation. The numerical calculations are presently limited to a small number of protons but go beyond the rotating-wave approximation and allow one to take into account a dissipation term associated with the strong oscillating electric field. The next task of this theoretical model is to compute the excited states of the coherent system. A simplified interacting-qubit model gives evidence of collective transition energies larger than the single-oscillator spacing. It does not yet establish whether a realistic external pump can populate such collective excited states with appreciable probability, nor the overall pump-to-capture conversion efficiency in a realistic proton lattice. If suitable states can be populated, their de-excitation could make some electron-capture processes energetically possible, with generation of slow neutrons. This dynamical mechanism offers an alternative to the Widom–Larsen hypothesis of “heavy electrons”, and is closer to current models in mainstream physics. The consequences, in terms of nuclear transmutations, of neutron generation via electron capture would be similar to those already known in the literature.