Nuclear finite-size effects in light muonic atoms

The finite nuclear size corrections to the s-state energy levels of light muonic (or hydrogenic) atoms are calculated analytically through order (Zα)⁶. In addition to the usual expression of order (Zα)⁴, the (Zα)⁵, (Zα)⁶ and (Zα)⁶ log(Zα) contributions have been determined. These corrections have been separated into terms of nonrelativistic and relativistic orders. The results have been checked by solving perturbatively the exact eigenvalue equations of the Schroedinger and Dirac problems of a particle orbiting in the Coulomb field of a uniform charge distribution of fixed radius. Application is made to the case of the μ-⁴He atom. Finite-size contributions to the hydrogen Lamb shift and the relativistic recoil effect are briefly discussed.