I think the best critique of Widom-Larsen theory (I have seen) is this one. https://newenergytimes.com/v2/…13Tenfors-On-the-idea.pdf
I object to any theory which require 'renormalisation' (fudge factors) to fix the math, but more importantly these are Tenfors principal objections:-
3 Low-energy nuclear reactions
The title of Widom and Larsens article reads “Ultra low momentum neutron catalyzed nuclear reactions”. Such
reactions have been known for 80 years. They are utilized in fission reactors where the neutrons really acts as catalysts,
since each reaction produces new neutrons enabling a chain reaction.
The authors speculate about spontaneous collective motion in a room temperature metallic lattice of surface metallic hydride protons producing oscillating electric fields that renormalize the electron self-energy, adding significantly
to the effective mass and enabling production of low-energy neutrons.
A number of objections can be raised against their treatment of the subject:
1) While proton oscillations and surface plasmon polaritons can exist in metal lattices, they need energy to grow!
To reach the necessary electron mass enhancement, each oscillating electron needs 0.78MeV, which is not readily
available in a room temperature metal lattice.
2) The fluctuating electric field evaluated from the neutron scattering data on proton oscillation frequency and
displacement is far from adequate for reaching the threshold for neutron production. In the neutron scattering
experiment, the proton energy appears to be higher than room temperature thermal. The energy in this case most
likely is provided by the diagnostic neutron beam.
3) The authors point out the importance of avoiding the Coulomb barrier, but they provide no discussion of the
energy needed. The electrons will lose energy by competing interactions in the metal lattice. Only a small fraction
of the electrons may produce neutrons and we must take all competing mechanisms into account. Reaching the
threshold probably requires a substantial energy input by particle beams or infrared lasers.
4) Widom and Larsens exercise with the stationary electric field could have led to the correct electric field strength
using the measured frequency and displacement in eq. (6), but they failed to realize that. They referred to violation
of the Born-Oppenheimer approximation to explain the lack of Coulomb screening needed to get the high charge
densities assumed. However, the positive charges in the lattice nuclei and the protons cannot be neglected to
the extent the wish, as demonstrated by the neutron scattering data. The stationary field approach also caused
confusion since they omitted the time dependence in their eq. (16), which obscured the relation between the electric
field and the electron oscillation energy.
5) They referred to violation of the Born-Oppenheimer approximation to explain the lack of Coulomb screening needed
to get the high charge densities assumed. However, the positive charges in the lattice nuclei and the protons cannot
be neglected to the extent they wish, as demonstrated by the neutron scattering data.
6) They do not disclose the measured frequency explicitly, in these comments it is evaluated from eqs. (1) and (3).
In a later publication [2] the authors note that “for metallic hydride surfaces upon which plasma oscillations exist,
typical values for the surface plasmon polariton frequencies are in the range (¯hΩ/e) ≈ (5 − 6) × 10−2 V”. This
yields Ω ≈ (8 − 10) × 1013 s−1.
7) Their habit of mixing SI and Gaussian units in the equations in the equations obscures the evaluation process.
In addition to the energy threshold for neutron production, we must look at the cross-section for the reaction. This
is not discussed in [1], but in [2]; the authors provide an estimate of vσ in the limit of vanishing initial relative
velocity. However, with relativistic electrons the reaction rate would be severely reduced. A relativistic electron
must come very close to a proton to be captured. At larger distances the electron will transfer energy to the proton.
The behaviour of beta decay of a neutron and the reverse process ˜e + p → n + νe, due to the weak interaction, in the
presence of an electric field has been considered in detail in the literature [3,4]. A compact expression for the total
probability for a process perturbed by a laser field was investigated as a function of the field intensity and frequency.
The main conclusion is that even in strong laser fields the effects are negligible.
not self centered as so many french examples....
