Coulomb-Recoil-Implantation Mössbauer Experiments withGe73

Abstract

The 67.03-keV state of ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ge}$ has been populated by Coulomb excitation and the recoiling excited nuclei implanted into Cr, Fe, and Cu backings. Nuclear and solid-state properties of ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ge}$ have been determined by studying the de-excitation $\gamma$ rays by Mössbauer techniques. The present measurements yield a lifetime of (2.68±0.14)×${10}^{-9\mathrm{}}$ sec, and favor a spin of $\frac{7}{2}$ for the 67.03-keV excited state. The measured isomer shift between pure germanium and Ge${\mathrm{O}}_2$ is + 1.0±0.1 mm/sec, and electron densities calculated for these two cases imply that the radius of the excited state is larger than that of the ground state, and $\frac{\Delta R}{R}=+0.9\mathrm{}\times {10}^{-3\mathrm{}}$ in reasonable agreement with calculations based on the pairing-plus-quadrupole model. To calculate the recoilless fraction $f$ of an impurity atom, a simple model with spring forces between nearest neighbors is introduced. In each case the effective spring constant for the impurity, as derived from the observed $f$ value, is weaker than that of the host lattice. A remarkable difference was found between $f$ values for tetragonal and hexagonal Ge${\mathrm{O}}_2$, namely $f\left(\mathrm{tetr}\right)\sim 5f\left(\mathrm{hex}\right)$.