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

[Laurence Marks]

Hmmmmmmmm.

There are some nasty numerical issues about how to treat the density
near the nucleus in Wien2k. I spent some months trying to work out
what is "right" to get better results with MSR1a for the forces, and
ended up giving up.

May I suggest a simple test. Try changing the R0 value that you are
using for the atoms, and perhaps adjust NPT, using clminter to
interpolate. Then see how the hyperfine results change.

On Sun, Jan 19, 2014 at 9:16 AM, pieper <pieper at ifp.tuwien.ac.at> wrote:
> 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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-- 
Professor Laurence Marks
Department of Materials Science and Engineering
Northwestern University
www.numis.northwestern.edu 1-847-491-3996
"Research is to see what everybody else has seen, and to think what
nobody else has thought"
Albert Szent-Gyorgi