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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