Use of harmonic oscillator potential in the analysis of muonic transition energies

Energy levels: 1s _1/2, 2p _1/2, 2p _3/2, 3d _3/2, and 3d _5/2 of the muon in the spherical nuclei:¹²⁰Sn,¹⁹⁷Au and²⁰⁸Pb have been calculated under the assumption of harmonic oscillator potential. The levels are corrected for vacuum polarisation. The agreement with experimental values is better than 0·5%. An accurate method of solving the Dirac equation to obtain the energy eigenvalues is outlined. The importance of choosing the ‘classical turning point’ as the radius for matching the interior and exterior solutions is discussed.