We calculate the hyperfine-structure properties of the low-lying states in ${}^{69}\mathrm{Ga}$ and ${}^{71}\mathrm{Ga}$ using the relativistic coupled-cluster method at the singles and doubles 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 ${}^{69,71}\mathrm{Ga}$ [Daly and Holloway, Phys. Rev. 96, 539 (1954)] and refine the nuclear magnetic octupole moments of these two isotopes. The refined values $\mathrm{\Omega }\left({}^{69}\mathrm{Ga}\right)=0.123\left(9\right){\mu }_N\times b$ and $\mathrm{\Omega }\left({}^{71}\mathrm{Ga}\right)=0.165\left(15\right){\mu }_N\times b$ are about 13% and 12% larger than the earlier results reported by Daly and Holloway. By providing an independent ab initio determination, the present results offer a reliable set of reference values for the magnetic octupole moments of ${}^{69,71}\mathrm{Ga}$, which will benefit both future high-precision measurements and nuclear-structure calculations.

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• Atomic & molecular structure
• Electron correlation calculations for atoms & ions
• Fine & hyperfine structure
• Nuclear shapes and moments