First-excited state g factors in the stable, even Ge and Se isotopes

Abstract

Transient-field $g$-factor measurements in inverse kinematics were performed for the first-excited states of the stable, even isotopes of Ge and Se. The $g$ factors of $^{74}\mathrm{Ge}$ and $^{74}\mathrm{Se}$ were measured simultaneously using a cocktail beam, which eliminates most possible sources of systematic error in a relative $g$-factor measurement. The results are $g(^{74}\mathrm{Se})/g(^{74}\mathrm{Ge})=1.34(7), g(^{70}\mathrm{Ge})/g(^{74}\mathrm{Ge})=1.16(15), g(^{72}\mathrm{Ge})/g(^{74}\mathrm{Ge})=0.92(13), g(^{76}\mathrm{Ge})/g(^{74}\mathrm{Ge})=0.88(5), g(^{76}\mathrm{Se})/g(^{74}\mathrm{Se})=0.96(7), g(^{78}\mathrm{Se})/g(^{74}\mathrm{Se})=0.82(5), g(^{80}\mathrm{Se})/g(^{74}\mathrm{Se})=0.99(7)$, and $g(^{82}\mathrm{Se})/g(^{74}\mathrm{Se})=1.19(6)$. The measured $g$-factor ratios are in agreement with ratios from previous measurements, despite considerable variation in previous reported absolute values. The absolute values of the $g$ factors remain uncertain, however, the Rutgers parametrization was used to set the transient-field strength and then compare the experimental $g$ factors with shell-model calculations based on the JUN45 and jj44b interactions. Modest agreement was found between experiment and theory for both interactions. The shell-model calculations indicate that the $g({2}_{1}^{+})$ values and trends are determined largely by the balance of the spin carried by orbital motion of the protons.