Energy levels of a muonic atom

The energy levels of a muonic atom, taking electron screening into account, are determined by directly solving the Dirac equation in a screened Coulomb potential of the Allis-Morse type. The non-relativistic limit of the result agrees with the values obtained by solving the Schroedinger equation for a muon in such a potential. The deviation from the Coulomb case is of the form 3 exp(-xZm/mxe), where x approximately 2 to 7 for the 1Ssub(1/2) state and is thus small if values of a1 are taken from the tables of Allis and Morse. However, these values fitted to electron-scattering experiments may not be relevant for muonic atoms so that experimental determination of a1 for muonic atoms is required. If a1 should be smaller, the perturbation of the Coulomb levels would be greater, especially for the outer shells, and one could vary the parameter a1 to fit the results with experiments. (author)