Refined nuclear magnetic octupole moment of In113 and In115

The refined values of the magnetic octupole moments of ¹¹³In and ¹¹⁵In 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 5p3/2 state of ¹¹³In and ¹¹⁵In [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 ¹¹³In and ¹¹⁵In nuclei are extracted to be Ω(¹¹³In)=0.456(44)4pt0exμN×b, and Ω(¹¹⁵In)=0.447(42)4pt0exμN×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 ¹¹⁵In nuclei to be Q(¹¹⁵In)=0.758(12)b by combining our theoretical result and the measured value for the HFS constant of the 5p3/2 state. Our results are compared with available experimental and theoretical results.