We calculate hyperfine structure intervals $\mathrm{\Delta }{E}^{hfs}\left(2P_{1/2}\right)$ and $\mathrm{\Delta }{E}^{hfs}\left(2P_{3/2}\right)$ 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 the projection operators on states with definite quantum numbers of total atomic momentum $F$ and total muon momentum $j$. We take into account the vacuum polarization, relativistic, quadruple, and structure corrections of order ${\alpha }^4$, ${\alpha }^5$, and ${\alpha }^6$. The obtained numerical values of hyperfine splittings can be used for a comparison with future experimental data of the CREMA Collaboration.

• Received 21 October 2019

DOI:https://doi.org/10.1103/PhysRevA.100.062513