[Wien] Effect of finite nucleus on electron density at the nucleus

[pieper]

Dear Amlan Ray,

in your initial mail you wrote that at the moment the state of the art 
in electron capture is to use 'the value of the electron density at the 
first mesh point'. If that is really the case my guess is that your 
problems are due to this procedure rather than to the influence of a 
finite size of the nucleus on the wave function.

It is well known that such an extrapolation from the innermost mesh 
point does not work for the hyperfine field. Bluegel et al. explain in 
their aforementioned PRB that a consistent, relativistic zero-order 
approximation of the electron density is necessary - and that it does 
the trick. At least for the hyperfine field the problem is not the 
influence of the finite size nucleus on the wave function, but how the 
electron density is calculated from the wave function.

What you apparently need is the electron density at the nucleus. Perhaps 
an average density would be sufficient (it is for the hyperfine field). 
With my comment I wanted to point out that Wien2k already provides you 
with such an average electron density because hyperfine fields are 
calculated. In case.scf the densities of the two spin channels are 
printed in the two lines above :HFF001: ... (for atom number 1).

I would expect that this value is much better suited to describe 
electron capture than the density at the innermost point of the radial 
mesh. An obvious problem might be that the Thomson radius of the sphere 
taken into account for the hyperfine field is roughly ten times the 
actual nuclear radius (also see Bluegel et al.) Maybe WIEN2k's averaging 
can be improved for your purposes in a cheap way by feeding the 
subroutines calculating the hyperfine field the actual nuclear radius 
instead of the Thomson radius.

I might be wrong (and would appreciate to know why), but I doubt that 
calculating the DFT with finite size nuclei makes sense until something 
like such a proper expectation value replaces the extrapolation from the 
innermost mesh point .

Best regards

Martin Pieper






Am 18.01.2014 16:04, schrieb Amlan Ray:
> Thank you very much for all the comments I received from this forum
> regarding my earlier question. Let me describe my problem in some more
> detail. The electron capture nuclear decay rate is directly
> proportional to the electron density at the nucleus unlike the isomer
> shift problem. The observed percentage increase of the electron
> capture nuclear decay rate (Delta_lambda/lambda) under compression
> (such as the study of electron capture decay rate of 7BeO lattice
> under compression) is much larger (by a factor of 3-6) than the
> estimates from WIEN2K and other calculations. The discrepancy
> increases by many fold in the case of heavier elements. However all
> those calculations use a point nucleus. I think the calculated
> percentage increase of the electron density at the nucleus due to the
> compression of the lattice could increase significantly if a finite
> nucleus is used. One reason for the increase of (Delta_Lambda/Lambda)
> could be the significant reduction of the electron density at the
> nucleus in the case of a finite nucleus as shown for a particular
> moment of the electron density (Phys. Rev A81, 032507, (2010) sent to
> me by Stefaan Cottenier]. So this is my motivation for thinking about
> using a finite nucleus in WIEN2K.
> 
> Can you please tell me which subroutines of WIEN2K should be modified
> for introducing a finite nucleus? Of course, relativistic calculations
> have to be done.
> 
> With best regards
> Amlan Ray
> Variable Energy Cyclotron Center
> Kolkata, India
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