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

[Peter Blaha]

For hyperfine fields we follow Bluegels work and average the spin 
density as mentioned below.

However, I'm not aware about a similar argument for isomer shifts (and 
I'm not familiar with electron capture).
Clearly, for isomer shifts it might be that the problem is fixed by 
taking an appropriate alpha when converting into mm/s.

In any case, the potential due to a finite nucleus would add another 
dimension.


On 01/17/2014 03:38 PM, pieper wrote:
>
> I am curious about Peter's answer:
>
> I would have expected that the problem of nuclear decay through electron
> capture is very closely related to the one of calculating hyperfine
> parameters like isomer shift or hyperfine field. At first sight the
> calculation of these parameters suffers from the same problem of a
> nuclear point charge or spin.
>
> I did not follow the development of calculations of the isomer shift
> which is given by the total electron density at the nucleus, but for the
> hyperfine field I always considered the work of Blügel et. al (Phys.
> Rev. B, 1987, volume 35, p. 3271) to be very illuminating. They show
> that the electron spin density should be averaged over a finite volume
> and calculate the appropriate (Thomson) radius of that volume. I would
> have expected that basically the same argument works for electron capture.
>
> To my knowledge this averge of the electron density is, in fact, whats
> done in Wien2k to calculate the the hyperfine fields (Fermi-contact and
> orbital)? In that case it might be useful not to take the electron
> density at the innermost mesh point, but the sin-up and -down densities
> calculated for the hyperfine fields.
>
> Best regards,
>
> Martin Pieper
>
>
>
>
> Am 17.01.2014 14:32, schrieb Peter Blaha:
>> In principle you are absolutely right. The question is only, for wich
>> property does it really matter.
>>
>> At the moment I do not have plans to put a finite nucleus into the
>> code myself.
>>
>
>
>
>> On 01/17/2014 01:03 PM, Amlan Ray wrote:
>>> Dear Prof. Blaha,
>>> I use WIEN2K code for calculating electron density at the nucleus to
>>> determine the change of electron capture nuclear decay rate in different
>>> environments. WIEN2K uses a point nucleus and I use the value of the
>>> electron density at the first mesh point as given by the code. I am
>>> interested to know the effect of the finite size of the nucleus on the
>>> electron density at the nucleus. Since Dirac wavefunction of
>>> s-electron becomes infinity at r=0 for a point nucleus, the effect of
>>> considering a finite nucleus could be significant for calculating the
>>> electron density at the nucleus.
>>> I was wondering if the effect of a finite nucleus might be included in
>>> an upcoming version of WIEN2K. Please let me know if there is any such
>>> plan.
>>> With best regards
>>> Amlan Ray
>>> Variable Energy Cyclotron Center
>>> Kolkata, India
>>>
>>>
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-- 

                                       P.Blaha
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
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