$Ab$ $initio$ calculation of hyperfine-structure properties to extract nuclear magnetic octupole moments of ${}^{69}$Ga and ${}^{71}$Ga

Abstract

We calculate the hyperfine-structure properties of the low-lying states in ${}^{69}$Ga and ${}^{71}$Ga using the relativistic coupled-cluster method at the singles and doubles (RCCSD) level. The properties include the first-order hyperfine constants and the second-order corrections arising from off-diagonal hyperfine interactions. Based on our theoretical results, we reanalyze the previous hyperfine-splitting measurements of the $4p_{3/2}$ state in ${}^{69,71}$Ga [R. T. Daly and J. H. Holloway, Phys. Rev. 96, 539 (1954)], and refine the nuclear magnetic octupole moments of these two isotopes. The refined values $\Omega {(}^{69}\mathrm{Ga})=0.123(9){\mu }_N\times b$ and $\Omega {(}^{71}\mathrm{Ga})=0.165(15){\mu }_N\times b$ are about 13\% and 12\% larger than the earlier results reported by Daly and Holloway. By providing the first independent \emph{ab initio} determination, the present results offer a reliable set of reference values for the magnetic octupole moments of ${}^{69,71}$Ga, which will benefit both future high-precision measurements and nuclear-structure calculations.