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 Schrödinger Equation for a muon in such a potential. The deviation from the Coulomb case is of the form 3 exp (− xZm / m e ), where x ≈ 2 to 7 for the 1 S 1/2 state and is thus small if values of a 1 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 a 1 for muonic atoms is required. If a 1 should be smaller, the perturbation of the Coulomb levels would be greater, especially for the outer shells, and one could vary the parameter a 1 to a 1 to fit the results with experiments.