Precision calculation of hyperfine structure of $^{7,9}$Be$^{2+}$ ions

TL;DR

This paper presents highly precise calculations of the hyperfine structure of $^{7,9}$Be$^{2+}$ ions using NRQED, significantly improving accuracy and proposing a new method to study Be nuclear properties through spectral analysis.

Contribution

The study provides the most accurate hyperfine splitting results for $^{9}$Be$^{2+}$ and introduces a novel spectral scheme to determine Be nuclear properties like the Zemach radius.

Findings

Achieved two orders of magnitude improvement in hyperfine splitting accuracy for $^{9}$Be$^{2+}$.

Studied the nuclear electric quadrupole contribution to hyperfine structure.

Proposed a new spectral method to determine Be nuclear properties.

Abstract

The hyperfine structures of the $2\,^3\!S_1$ and $2\,^3\!P_J$ states of the $^7$Be$^{2+}$ and $^9$Be$^{2+}$ ions are investigated within the framework of the nonrelativistic quantum electrodynamics (NRQED). The uncertainties of present hyperfine splitting results of $^9$Be$^{2+}$ are in the order of several tens of ppm, where two orders of magnitude improvement over the previous theory and experiment values has been achieved. The contribution of nuclear electric quadrupole moment to hyperfine splitting of $^7$Be$^{2+}$ has been studied. A scheme for determining the properties of Be nuclei in terms of Zemach radius or the electric quadrupole moment based on precise spectra is proposed, and it opens a new window for the study of Be nuclei.