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Sent: Monday, September 11, 2006 15:19
To: Boss, Pam SPAWAR
Cc: Rees, Dave SPAWAR; Boss, Roger SPAWAR; Gordon, Frank SES SPAWAR 230
Subject: Re: Metal Hydride cathode catalysis of e + p -> nu + n
I've finished looking through the paper.
Important qualifier: it has been awhile since I have thought about these types of calculations, so take this with a grain of salt.
This paper uses standard quantum field theory (nonrelativistic limit) and various uniformity and simplest-case-type assumptions to calculate an estimate of the rate for p + e- -> nu (neutrino) + n (neutron). The techniques used are all conventional and frequently used. There are a number of simplifying assumptions made that then allow a simple closed-form estimate. The final estimate is that the rate is of order 10^13 to 10^14 per unit area per unit time when a cutoff parameter (expressed in terms of effective electron mass) is exceeded. It is claimed that this is compatible with observed rates.
The basic idea is straightforward and closely related to basic semiconductor physics where "holes" (vacancies in a lattice) can be treated as massive charged particles - the net effect of the medium is to add an "effective mass" (to a pretty good first-order approximation). Normally one would not expect a significant transition rate because the reaction is energy-forbidden (mass(p) + mass(e-) <mass(n) by a significant amount). However, due to the strong currents and surface effects at a metal hydride cathode, there will be significant radiation field interaction with electrons in this zone. This radiation field interaction, to lowest order, can manifest as an increased "effective mass" for electrons. If the effect is great enough, the reaction can proceed.
This idea seems reasonable. The authors use a four-fermi vertex interaction to estimate the rate. I followed through the work and all calculations seemed to be consistent with standard practice, and to be correct so far as I can tell. I can't say that I followed every factor of pi through.
The baryon operators (p, n) are handled in terms of isospin, should be a good approach for the nonrelativistic regime here. A standard phase space integration is used to compute the transition rate; I don't see any problems with it.
The basic idea seems reasonable; I don't see any reason it shouldn't be correct. In fact, it is the most obvious way to proceed.
All the calculations seem to be correct as far as I can tell. If there is any problem (it seems to me), it is in the assumptions made for simplification, or in something subtle that would prevent the sort of straightforward approach the authors use. Thus I list the key assumptions I saw and my guess as to their impact here.
1. "if there are n(2) ~ 10^15/cm^2 effective (e*- p+) pairs per unit surface area [in the surface zone] ..."
- I haven't a clue as to if this is reasonable or not (chemists might know better!). It would at least seem to be compatible with Avogadro's number, for what that is worth. BTW, this number is key to the estimated rate.
- Likely fine. Slight possibility of issues with mass(W).
3. Surface isotopic spin wave approach
- Seems good to me.
4. Patch size for the isotopic spin wave
- I don't know how to estimate this. A good distribution for this would likely permit a neutron energy-spectrum estimate, which would be a good verification tool.
5. The effective mass wave function transformation
- I can't see why this wouldn't be correct
6. Proton spins are uncorrelated and free neutron density is dilute
- Neutron density dilute almost certainly correct. Proton spins - I don't know.
7. "The calculation of K depends on the detailed physical properties of the cathode surface as well as the flux per unit area per unit time of electrons ..." "In the most simple model, let us consider a smooth surface ..."
- Gory details could be important, as authors note.
8. "... let us consider ... electron currents ... via the mass renormalization parameter beta as defined in eq. 46."
- Basically after lots of calculation and some simplifying assumptions, the authors just *assume* that the mass renormalization approach is the way to go. This happens between equations 61 and 62 and is key to the result. I suspect the authors are right ( can't see why this wouldn't be correct, as per 5 above), but more work could go into this step.
9. Infrared/Ultraviolet cutoffs
- In such a radiative coupling rich environment, cutoffs could impact this approach. In the strictly nonrelativistic four-point vertex, I think is probably OK. I think.
Techniques and calculations are straightforward, and (as far as I can tell) correct. There could be some assumptions that need to be dealt with in more detail (could spell trouble). My "feel" is that they are OK.
The paper looks good to me. It's a clever idea, I think (clever ideas are always obvious in hindsight).