Coherent Oscillations of Protons in Hydrogen-loaded Metals
Abstract
We review recent calculations and numerical simulations showing the formation of coherent states of protons in hydrogen-loaded metals with a cubic crystal lattice. In these states protons oscillate coherently at frequencies of the order of 1013 Hz 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. There are strong indications that in those states protons can be excited by an external pump to energies much larger than those achievable by single incoherent protons in condensed matter. Such energies are large enough to make possible some electron-capture processes, 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 predicted by Widom and Larsen, plus several other processes like those recently re-examined by Metzler et al.
Versions
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BibTeX
@misc{modanese2026coherent,
title = {{Coherent Oscillations of Protons in Hydrogen-loaded Metals}},
author = {G. Modanese},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.21452},
eprint = {2608.21452},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.21452},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Coherent Oscillations of Protons in Hydrogen-loaded Metals
AU - G. Modanese
PY - 2026
DA - 2026/08/20
PB - arXiv
DO - 10.48550/arxiv.2608.21452
UR - https://arxiv.org/abs/2608.21452
AB - We review recent calculations and numerical simulations showing the formation of coherent states of protons in hydrogen-loaded metals with a cubic crystal lattice. In these states protons oscillate coherently at frequencies of the order of 10^13 Hz 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. There are strong indications that in those states protons can be excited by an external pump to energies much larger than those achievable by single incoherent protons in condensed matter. Such energies are large enough to make possible some electron-capture processes, 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 predicted by Widom and Larsen, plus several other processes like those recently re-examined by Metzler et al.
ER -