Hyperfine structure of P states in muonic ions of lithium, beryllium and boron

TL;DR

This paper calculates the hyperfine structure intervals of P-states in muonic lithium, beryllium, and boron ions, incorporating various quantum corrections, to aid future experimental comparisons.

Contribution

It introduces a tensor method of projection operators to compute hyperfine splittings in muonic ions, including higher-order corrections.

Findings

Calculated hyperfine splittings for muonic P-states in lithium, beryllium, and boron.

Provided numerical values for future experimental validation.

Enhanced theoretical understanding of muonic ion hyperfine structures.

Abstract

We calculate hyperfine structure intervals $\Delta E^{hfs}(2P_{1/2})$ and $\Delta E^{hfs}(2P_{3/2})$ for P-states in muonic ions of lithium, beryllium and boron. To construct the particle interaction operator in momentum space we use the tensor method of projection operators on states with definite quantum numbers of total atomic momentum F and total muon momentum j. We take into account vacuum polarization, relativistic, quadruple and structure corrections of orders $\alpha^4$, $\alpha^5$ and $\alpha^6$. The obtained numerical values of hyperfine splittings can be used for a comparison with future experimental data of the CREMA collaboration.