Calculation of Isomer Shift in Mössbauer Spectroscopy

Abstract

The approximations normally used in the calculation of the isomer shift are compared with the exact expressions using Dirac-Slater orbitals and a three-parameter Fermi-type nuclear charge distribution. The nonuniformity of the electronic density over the nuclear volume affects the results. Different choices of the nuclear surface thickness $t$ and the radius $c$ in the protonic density ${\rho }_N\mathrm{}\left(r\right)\mathrm{}$ also affects the isomer shift differently even though the values are chosen to yield a given value of $\Delta 〈r^2〉$. The change in the electronic charge density which is caused by the alteration of ${\rho }_N\mathrm{}\left(r\right)\mathrm{}$ in the ground state and excited state of the nucleus is discussed using two extreme models and the possible influence on the observable isomer shift is estimated.