Relativistic coupled-cluster-theory analysis of the hyperfine interaction of Ra$^{+}$ isotopes

TL;DR

This paper uses relativistic coupled-cluster theory to analyze hyperfine interactions in Ra$^{+}$ isotopes, providing new calculations of hyperfine constants and nuclear moments, and assessing the potential to detect nuclear octupole effects.

Contribution

The study applies relativistic coupled-cluster methods to compute hyperfine constants and nuclear moments in Ra$^{+}$, offering improved theoretical insights and experimental relevance.

Findings

Calculated hyperfine constants agree with experimental data.

Extracted nuclear quadrupole moments for several Ra isotopes.

Assessed the detectability of nuclear octupole effects in hyperfine measurements.

Abstract

Hyperfine-structure constants of odd Ra$^{+}$ due to the interactions of nuclear magnetic dipole, electric quadrupole, and magnetic octupole moments with the electrons are investigated in the framework of relativistic coupled-cluster method within single- and double-excitation approximation. The calculated energies and magnetic dipole hyperfine-structure constants $A$ exhibit a good agreement with available experimental values. Combining with the experimental electric quadrupole hyperfine-structure constant, we also extracted the electric quadrupole moments $Q$ of $^{209,211,221,223}$Ra. Our $Q$($^{221}$Ra) and $Q$($^{223}$Ra) are consistent with the referenced values from a semi-empirical analysis (Z. Phys. D: At., Mol. Clusters 11, 105 (1988)), but $Q(^{211}$Ra)=$0.33(2)$ is smaller than the referenced value $0.48(4)$ by about 30\%. Furthermore, we also performed a procedure for assessing the contributions of magnetic octupole moment to the hyperfine splitting. The sensitivity of hyperfine-structure interval measurements in $^{223}$Ra$^{+}$ that can reveal the effect caused by the nuclear octupole moment are found to be on the order of kHz.