Refined nuclear magnetic octupole moment of ${}^{113}\mathrm{In}$ and ${}^{115}\mathrm{In}$

The refined values of the magnetic octupole moments of ${}^{113}\mathrm{In}$ and ${}^{115}\mathrm{In}$ are obtained by combining high-precision atomic calculations with the corresponding hyperfine structure (HFS) spectrum. We perform ab initio calculations of HFS properties for the low-lying states of the In atom using the single- and double-approximated relativistic coupled-cluster method. The HFS properties includes first-order HFS constants and the second-order magnetic dipole-magnetic dipole, magnetic dipole-electric quadrupole, and electric quadrupole-electric quadrupole effects caused by the off-diagonal hyperfine interaction (HFI). Based on our theoretical results, we reanalyze the previously measurements of hyperfine splitting in the $5p_{3/2}$ state of ${}^{113}\mathrm{In}$ and ${}^{115}\mathrm{In}$ [T. G. Eck and P. Kusch, Phys. Rev. 106, 958 (1957)], determining the corresponding hyperfine-structure constants $A, B$, and $C$. By combining these undated HFS constants and our theoretical results, the magnetic octupole moments of ${}^{113}\mathrm{In}$ and ${}^{115}\mathrm{In}$ nuclei are extracted to be $\mathrm{\Omega }\left({}^{113}\mathrm{In}\right)=0.456\left(44\right){\mu }_N\times b$, and $\mathrm{\Omega }\left({}^{115}\mathrm{In}\right)=0.447\left(42\right){\mu }_N\times b$, respectively. The refined values of the magnetic octupole moments are about 21% smaller than the previously reported results by Eck and Kusch [T. G. Eck and P. Kusch, Phys. Rev. 106, 958 (1957)]. Additionally, we also determine the electric quadrupole moment of ${}^{115}\mathrm{In}$ nuclei to be $Q\left({}^{115}\mathrm{In}\right)=0.758\left(12\right)b$ by combining our theoretical result and the measured value for the HFS constant of the $5p_{3/2}$ state. Our results are compared with available experimental and theoretical results.

Figure 1

Schematic diagram of HFS in ${}^{115}\mathrm{In}$ for states of $5p_{3/2}$ and $6p_{3/2}$, where $\mathrm{\Delta }{E}_{F{F}^{\prime }}$ denotes the energy difference between two adjacent hyperfine levels determined by experiment [16, 17].