Systematics of the pressure dependence of the electron density at the nucleus for the elements Ag through Te: Pressure dependence of the Mössbauer isomer shift for Sn and Sb

Experimental Mössbauer isomer shift studies have shown that when $\beta -\mathrm{Sn}$ is compressed, the charge density $\rho \mathrm{}\left(0\right)\mathrm{}$ at the nucleus decreases, viz., $\frac{\partial \ln \rho \mathrm{}\left(0\right)\mathrm{}}{\partial \ln V}>0\mathrm{}$. This fact suggested a study of the systematics of $\frac{\partial \ln \rho \mathrm{}\left(0\right)\mathrm{}}{\partial \ln V}$ for the Ag row of the Periodic Table. We have calculated $\frac{\partial \ln \rho \mathrm{}\left(0\right)\mathrm{}}{\partial \ln V}$ for the elements Ag through Te in a Hartree-Dirac-Wigner-Seitz approximation. Exchange is treated through an exchange potential. These calculations indicate that both valence- and core-electron contributions play a role in determining $\frac{\partial \ln \rho \mathrm{}\left(0\right)\mathrm{}}{\partial \ln V}$. In the Wigner-Seitz model, a positive sign for $\frac{\partial \ln \rho \mathrm{}\left(0\right)\mathrm{}}{\partial \ln V}$ for $\beta -\mathrm{Sn}$ (i.e.,the sign which agrees with experimental high-pressure Mössbauer isomer shift studies) is obtained only if the exchange multiplier lies in the range $1.3\le \zeta \le 1.5$, where $\zeta =1.5\mathrm{}$ corresponds to full Slater exchange. These Wigner-Seitz model calculations indicate a negative sign for $\frac{\partial \ln \rho \mathrm{}\left(0\right)\mathrm{}}{\partial \ln V}$ for Ag, Cd, and In, and a positive sign for this derivative for Sb, and Te. The sign for Sn depends on $\zeta$, as indicated.