Overview
A recent study involved an ab initio calculation of hyperfine-structure properties for low-lying states in the isotopes $^{69}$Ga and $^{71}$Ga. The research specifically employed the relativistic coupled-cluster method at the singles and doubles (RCCSD) level to determine these properties. Based on the theoretical outcomes, a reanalysis of historical hyperfine-splitting measurements was conducted, leading to a refinement of the nuclear magnetic octupole moments for both $^{69}$Ga and $^{71}$Ga.
Approach
The methodology centered on the application of the relativistic coupled-cluster method, specifically at the singles and doubles (RCCSD) approximation level. This approach was utilized to calculate two primary categories of hyperfine-structure properties:
- First-order hyperfine constants.
- Second-order corrections, which arise from off-diagonal hyperfine interactions.
The calculations were performed for the low-lying states of both $^{69}$Ga and $^{71}$Ga isotopes. Following the generation of these theoretical results, the researchers used them to re-evaluate existing experimental data. Specifically, previous hyperfine-splitting measurements of the $4p_{3/2}$ state in $^{69,71}$Ga, originally reported by R. T. Daly and J. H. Holloway in Phys. Rev. 96, 539 (1954), were reanalyzed with the new theoretical framework.
Findings
The study yielded refined values for the nuclear magnetic octupole moments of the two gallium isotopes:
- For $^{69}$Ga, the refined nuclear magnetic octupole moment is $\Omega(^{69}\mathrm{Ga})=0.123(9)\,\mu_N\times b$.
- For $^{71}$Ga, the refined nuclear magnetic octupole moment is $\Omega(^{71}\mathrm{Ga})=0.165(15)\,\mu_N\times b$.
These refined values represent an increase compared to earlier results reported by Daly and Holloway. Specifically, the value for $^{69}$Ga is approximately 13% larger, and the value for $^{71}$Ga is approximately 12% larger than the previously published figures.
The current work represents the first independent ab initio determination of these specific properties.
Why This Matters
The results offer a reliable set of reference values for the magnetic octupole moments of $^{69,71}$Ga. These updated reference values are expected to be beneficial for both future high-precision measurements and nuclear-structure calculations related to these isotopes.