Change in Nuclear Radius upon Excitation forSn119,Sb121,Te125,I127,129, andXe129from Mössbauer Isomer Shifts

Abstract

The ratio $\frac{\delta 〈R^2〉}{〈R^2〉}$ for two nuclei can be obtained by comparing the measured isomer shifts for isoelectronic compounds of the two elements. Such a determination is fairly insensitive to the absolute value of the electron density at the nucleus. These ratios have been found sequentially for ${}_{}{}^{119}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{121}{}_{}{}^{}\mathrm{Sb}$, ${}_{}{}^{125}{}_{}{}^{}\mathrm{Te}$, ${}_{}{}^{127,129}{}_{}{}^{}\mathrm{I}$, and ${}_{}{}^{129}{}_{}{}^{}\mathrm{Xe}$. Taking $\frac{\delta 〈R^2〉}{〈R^2〉}$ for ${}_{}{}^{119}{}_{}{}^{}\mathrm{Sn}$ to be 2.4×${10}^{-4\mathrm{}}$, absolute values of $\frac{\delta 〈R^2〉}{〈R^2〉}$ for remaining nuclei have been found. The values are -14.6×${10}^{-4\mathrm{}}$, 1.9×${10}^{-4\mathrm{}}$, -4.8×${10}^{-4\mathrm{}}$, 6.2×${10}^{-4\mathrm{}}$, and 0.55×${10}^{-4\mathrm{}}$ for ${}_{}{}^{121}{}_{}{}^{}\mathrm{Sb}$, ${}_{}{}^{125}{}_{}{}^{}\mathrm{Te}$, ${}_{}{}^{127}{}_{}{}^{}\mathrm{I}$, ${}_{}{}^{129}{}_{}{}^{}\mathrm{I}$, and ${}_{}{}^{129}{}_{}{}^{}\mathrm{Xe}$, respectively. These values overlap those obtained directly by our electron-density calibrations, done individually, although they are different in some cases from earlier determinations. These results also supply a consistent set of values for the isomer shift per $5p$ or $5s$ electron for all five elements.