Theory of the Lamb shift in muonic helium ions

The Lamb shift (2P (1/2)-2S (1/2)) in muonic helium ions (mu (2) (3) )(+), (mu He-2/4)(+) is calculated taking into account the contributions of the order of alpha(3), alpha(4), alpha(5), and alpha(6). Special attention is paid to corrections for the polarization of the vacuum, as well as the structure and recoil of the nucleus. Numerical values 1259.8583 meV ((mu (2) (3) He)(+)) and 1379.1107 meV ((mu (2) (4) He)(+)) obtained for the shifts can be considered reliable estimates when compared to the experimental data of the CREMA collaboration.