Exact wave functions of bound μ − for calculating ordinary muon capture rates

The goal of the present contribution is twofold: (i) To compute exact wave functions for a muon bound in the extended Coulomb potential of a muonic atom by solving the Dirac equation within the context of genetic algorithms and neural network techniques using experimental finite-size charge-densities for the attracting nucleus. (ii) To calculate partial and total rates of the ordinary muon capture in various muonic atoms. In contrast to the majority of previous realistic calculations for μ−-capture rates, in our present work we utilize the above mentioned exact wave functions for a muon orbiting at the Is and 2p atomic orbits. The required many-body nuclear wave functions are obtained by diagonalizing the eigenvalue problem of the quasi-particle random phase approximation (QRPA).