Abstract
The Lamb shift (2P_{1/2}-2S_{1/2}) in the muonic helium ion (mu ^4_2He)^+ is calculated with the account of contributions of orders alpha^3, alpha^4, alpha^5 and alpha^6. Special attention is given to corrections of the electron vacuum polarization, the nuclear structure and recoil effects. The obtained numerical value of the Lamb shift 1379.028 meV can be considered as a reliable estimate for the comparison with experimental data.
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