As most know here, many prominent AHE / LENR reports might be explained by some plausible mechanism of how the 782 keV/c^2 mass-energy deficit is made up.
Earlier, discussed here on LF, in some detail from a quite different perspective, now linked at:
deBroglie's equation and heavy electrons
[I deduce we no longer need to advise "newbies" that the W-L theory ostensibly explains the "growing" a proton to neutron by adding such a heavy electron mechanism.]
As many here may know, and IMHO, deBroglie offers, a quite different explanation for "heavy" electrons, and that explanation might be, at least under "classical" QM, quite inconsistent with the usual "classical" relativistic interpretation. I believe the relativity-based explanations may be quite difficult-to-reconcile with observations. Recently it seems the theoreticians are seeking, and more recently, demanding difficult-to-imagine scenarios. And if Dr. Hagelstein's, and other JCMNS articles analyzing the energetics are correct, it may be quite impossible or insufficiently productive to seek "relativistic" explanations of increased mass suitable to accomplish LENR. This has apparently now evolved to a "received view" that is often used to brush away any low velocity heavy electron explanations of LENR / CF.
A little background: I was primed long ago, long before my science career, for discussions of QM via deBroglie from P.W. Atkins' Physical Chemistry (W.H. Freeman, 1978), especially the 2nd section "structure". And now I see a much later influence layered on the Atkins text: The (one volume version) of the 1993, 2nd edition of McGraw-Hill Encyclopedia of Physics (Sybil Parker, editor). In that tome was where I first saw the initial hints that led me to focus on one of the two core deBroglie equations, that is: lambda = h/p where "p" can be taken as classical momentum (that is: m dot v, as I understand it). Some key passages are there ca. p. 1112. I won't review that here, except to say that it appears that the by now classical QM uncertainty relationship, that is a reciprocal "complementarity" relationship of position (distributed as "wavelength" in lambda) with momentum distribution as "p".... can indeed be further decomposed (classical Newton: p=mv) to allow not only velocity uncertainty, but mass fluctuation, at least in one vectorial pairing, in that article, say the "x" axis.
With the greatest respect for some of the living giants in the CF field, it seems such a strictly relativistic explanation of mass gain, at least at first view, is quite the contrived situation. So much so, that I suspected it a "strawman" to have electrons in the conduction band travel anywhere near the vacuum velocity of light.
But, here is another piece the older folks know well -- or maybe not: in view of Cerenkov / Cherenkov / Tcherenkov radiation, which is the emission of energy of the "forbidden" transluminal velocity as energy via photons induced by superluminal particle transit through transparent media. For example, velocity of light in pure water is about 0.76 of vacuum c in free space. Thus, with ANY superluminal transmission (ie. over c in the media) of any massive particle, we might "have our cake and eat it too", that is an increased relativistic mass at a relatively modest velocity compared to vacuum, AND the possibility of bonus energetic photon(s) accompaniment via Cherenkov.
[For "very newbies", Tcherenkov, Cherenkov, Cerenkov radiation, is the blue light seen in reactors and radwaste storage pools, the ostensible source of that blue light, for decades now, and I see at our never-to-be-trusted for controversial information, is Cherenkov's1934 explanation which led to Cherenkov's 1958 Nobel.]
With respect to what has been somewhat difficult-to-envision, this claimed as relativistic mass gain of 0.782 MeV/c^2 (to give a total of ~2.53 X the nominal CODATA rest electron mass of 0.511 MeV), I am deducing from ICCF 21 chats and other conversations with some of our most famous LENR scientists, and yet others perhaps not so famous, that if indeed this were possible, it is enabled by the much lower velocity c (from our external perspective, of course!) in some solid media, such as boron nitride (B4N or simply BN), graphene, diamond-like coatings, PTFE, Schott and Nikon high refractive index glasses and polymers, as well as barium glass, uranium glass, leaded glass and so on.
c in high refractive index materials such as boron nitride, boron carbide, as well as spodumene-like products, including high mp, low cost, quite transparent materials such as Corning's "Visions Ware", which is likely related to their "Vicor" glassware, or traditional transparent refractories such as fused or amorphous quartz, zirconia etc.
As one simple example, here is a little boron nitride paper:
https://ntrs.nasa.gov/archive/….nasa.gov/19870015584.pdf
therein is reported a refractive index of 1.65 to 1.67, taking a mean, gives c =1.8 X 10 ^8 m/s, v. ~3.0 X 10^8 in vacuo.
Finally, we see a conundrum of an almost ever-present structural theme in the more functional CF and LENR "cells" resolved and/or explained without resort to "crazy" stuff. That is the near universal presence of phase, state, field, or other structural interfaces / junctions in such cells . That may provide a plausible explanation of how a "situational transluminal velocity" could accomplish something constructive, even when there is too large a Fermi gap between the valence and conduction bands for metallic behavior. And proactively, we can now see that (perhaps) photons in transparent media are conjoined with electrons in nearby metallic media. Is there another parallel to Hagelstein's evocation and explanation of the Karabut data, or others theorists also seeking to explain the possible direct thermalization / "phononization", [to use an awkward term], of MeV photons?
Ponderables: What is the likelihood of a "heavy" conduction band electron making an excursion, or channeled, stripline or TIR fiber style, into adjacent non-conducting / insulating dielectric material? What happens to Cherenkov photons in that case? Are they plasmons? Can they participate as bosonically additive entities (that is, can they coherently elaborate optical pumping that might through Thomson-Compton or other mechanisms, further highly accelerate already electrostatically accelerated electrons?
As always, I admonish to "do you own due diligence". Think of energy and power densities that might accidentally occur. Don't want to lose these genii !!