Precision calculation of hyperfine structure and the Zemach radii of $^{6,7}$Li$^+$ ions

TL;DR

This paper provides a precise theoretical calculation of hyperfine structures and Zemach radii of $^{6,7}$Li$^+$ ions, revealing discrepancies with previous values and suggesting an anomalous nuclear structure for $^6$Li.

Contribution

The study introduces improved calculations of hyperfine structures and Zemach radii for lithium ions, highlighting significant deviations from prior measurements and nuclear physics estimates.

Findings

Zemach radii are larger than previous values for both isotopes.

Significant difference between calculated and nuclear physics-derived Zemach radius for $^6$Li.

Order of magnitude improvement in hyperfine splitting calculations for $^7$Li$^+$.

Abstract

The hyperfine structures of the $2\,^3\!S_1$ states of the $^6$Li$^+$ and $^7$Li$^+$ ions are investigated theoretically to extract the Zemach radii of the $^6$Li and $^7$Li nuclei by comparing with precision measurements. The obtained Zemach radii are larger than the previous values of Puchalski and Pachucki [\href{https://link.aps.org/doi/10.1103/PhysRevLett.111.243001}{Phys. Rev. Lett. {\bf 111}, 243001 (2013)}] and disagree with them by about 1.5 and 2.2 standard deviations for $^6$Li and $^7$Li, respectively. Furthermore, our Zemach radius of $^6$Li differs significantly from the nuclear physics value, derived from the nuclear charge and magnetic radii [\href{https://link.aps.org/doi/10.1103/PhysRevA.78.012513}{Phys. Rev. A {\bf 78}, 012513 (2008)}], by more than 6 sigma, indicating an anomalous nuclear structure for $^6$Li. The conclusion that the Zemach radius of $^7$Li is about 40\% larger than that of $^6$Li is confirmed. The obtained Zemach radii are used to calculate the hyperfine splittings of the $2\,^3\!P_J$ states of $^{6,7}$Li$^+$, where an order of magnitude improvement over the previous theory has been achieved for $^7$Li$^+$.