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

[Amlan Ray]

Dear Prof. Blaha,
Thank you very much for the detailed explanation regarding the treatment of the core 1s state of Be. I can now understand much better how the calculation for the core state is being done. If there is any paper or document describing the treatment of the core state in detail, then please give me the reference. As a beginner, I still have a few questions and shall be grateful for your reply. 
 
1) My understanding was that the total potential (electrostatic and exchange) inside a lattice approximately looks like a Muffin tin potential. For example, in the interstitial region, the electrostatic fields of the neighboring ions should approximately cancel out producing approximately a constant potential (zero field) region. I understand there is some fuzziness or arbitrariness in the determination of Muffin tin radius RMT and that part has no physical significance, but the overall picture of Muffin tin potential inside a lattice should have physical significance. Are you also saying the same thing? 
 
2) I did not know earlier that 1s wave function is seeing a continuous potential and the potential is continuing with a 1/r tail outside the Be sphere. However this would mean that 1s electrons are seeing the potential of a single Be ion outside RMT. But will not the potential outside the Be sphere be approximately constant because of the presence of other Be ions? If 1s and 2s electrons see different potentials outside the Be sphere, then they would not be orthogonal to each other. 
 
3) I have done calculations by treating both 1s and 2s states of Be as valence states, but I have not really understood how the code actually handled the situation. I understand that both 1s and 2s electrons will see the same complete potential inside the Be sphere and there would be spherical harmonic solutions. But outside the Be sphere, 2s electrons are seeing the potential of the interstitial region and are treated as approximately plane waves with a matching boundary condition at RMT. 
 
How will 1s electrons be treated outside the Be sphere, when they are also considered as valence electrons? They should also see the same constant potential in the interstitial region, but probably because of their higher energy should not be treated as plane waves. There would be the question of boundary condition at RMT for 1s valence electrons also. 
 
The absolute value of the total electron density at R0 increases by 0.07% to 0.14% if 1s is treated as a core state compared to as a valence state for Be. However the change of total electron density for Be at R0 for the compressed versus normal BeO lattice cases remain essentially the same whether we treat 1s as core or valence state. 
 
4) The energy of 1s core state always increases due to the compression of BeO lattice. From the physical point of view, I thought that the energy was increasing because the electrons were confined to a smaller region due to the compression. If the 1s electrons are spreading out, then what are the physical reasons for the increase of the energy of 1s electrons. 
 
With best regards
                                                                                         Amlan Ray
Address
Variable Energy Cyclotron Center
1/AF, Bidhan Nagar
Kolkata - 700064
India 

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