[Wien] Electron density at the nucleus (Electron capture nuclear decay rate work)

[Amlan Ray]

I have been reading all the messages about the electron density at the Be nucleus under compression and would like to say a few things. My background is in experimental nuclear physics and I am very interested to undertsand quantitatively the results of electron capture experiments in compressed material. WIEN2K is probably the best availabale code at this time for this purpose. Given my background, please excuse me if I make any incorrect statements. I shall be grateful if you would kindly point out my mistakes. 
 
1) Let me start with the Physics justification for thinking why Be 1s wave function should satisfy boundary conditions at the muffintin radius RMT(Be). As I understand, in this model, 1s electrons are seeing scf-potential of the crystal only within the Be sphere. Outside the Be sphere, it should see the potential of the interstitial region. Since there is an abrupt change of potential at the muffintin radius RMT(Be), so the wave function inside and outside the Be sphere should be different and there should be a matching boundary condition at RMT(Be). If we assume that outside the Be sphere, the 1s wave function should be that of a free Be ion, then it should be matched with the core wave function inside the Be sphere at RMT(Be). 
As a gross oversimplification, I suggested that the 1s wave function outside RMT(Be) might be taken as zero, because I thought that would be relatively easy to implement.(But I agree it was a wrong boundary condition.)  However  my main point is that the core wave function inside and outside the Be sphere should be different and there should be boundary conditions at RMT(Be). 
 
2) I think whether compression would delocalize 1s wave function should depend on the boundary condition applied. If the only boundary condition is that the core wave function would be zero at infinity, then of course, it will delocalize under compression. But probably there should be boundary conditions at RMT(Be).
 
3) I certainly agree that the tail of 1s wave function would experience more attractive potential when BeO is compressed. But I think that would affect the core wave function outside the Be sphere. It is not clear to me how that would affect the core wave function inside the Be sphere, particularly near the nucleus. The potential inside and outside the Be sphere is different and the wave functions should, in general, be different with a matching boundary condition at RMT(Be). 
 
4) I certainly agree that the contraction of 2s orbital would drive 1s orbital into expansion. But the reduction of 1s electron density at the nucleus is essentially independent of the muffintin radius used. I have done calculations of normal and compressed BeO cases keeping RMT(Be) the same in both the cases and have also done calculations by reducing RMT(Be) for the compressed case only. The change of 1s electron density at the nucleus remains the same always. The change of valence electrons in Be sphere is only 0.01 electrons and I can vary this number by adjusting RMT(Be). But that did not affect the change of 1s electron density at the nucleus. s-valence electrons in Be sphere can be made smaller for the compressed case by adjusting RMT(Be), but still the result did not change. So I think that the effect of 2s orbital contraction on 1s electron density at the nucleus is probably very small. 
 
5) I know about three experiments (done by different people) where the increase of electron capture rate by nuclei under compression was seen and the effect is much more than expected from valence electrons. 
 
With best regards
                                                                                     Amlan Ray
Address
Variable Energy Cyclotron Center
1/AF, Bidhan Nagar
Kolkata - 700064
India

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