Theoretical investigation of the isomer shifts of theSn119Mössbauer isotope

We solve the electronic structure problem self-consistently for a series of crystalline solids, containing Sn as a component, with the use of the first-principles scalar-relativistic linear muffin-tin-orbital method in the local-density approximation. The crystals considered are the two allotropes α-Sn and β-Sn as well as the compounds ${\mathrm{SnO}}_2$, ${\mathrm{SnMg}}_2$, SnSb, and SnTe. The derived band structure is discussed and compared to previous calculations and experimental information. By extension of the radial integration of the Dirac equation to well within the nuclear regime, the valence-electron contribution to the charge density on the nuclear site is obtained. Excellent agreement is found when comparing with experimental isomer shifts. A value of ΔR/R=(1.34±0.07)×${10}^{\mathrm{-}4}$ for the relative change of the radius of the ${}_{}{}^{119}{}_{}{}^{}\mathrm{Sn}$ nucleus upon excitation is deduced. The observed trends in the isomer shifts are interpreted on the basis of the decomposition of the crystal wave function into angular momentum character.