Model of Quasi-Nuclei for Mesoatoms

摘要

The model of quasi-nuclei composed of heavy particles with charges of opposite signs is applied to mesoatoms. It is shown that the description of a system composed of heavy particles in terms of quasi-nuclei is a natural consequence of the separation of variables in the kinetic energy operator of the system with the use of the Jacobi coordinates, one of which is the difference in the radius vectors of the heavy particles. A model of a point quasi-nucleus is considered and the energy correction with regard for the finite size of a quasi-nucleus is calculated. A one-parameter model of a quasi-nucleus with a quantum defect is proposed for calculation of the excited energy levels of systems containing quasi-nuclei. The application of the results obtained to heliummuon-electron mesoatoms shows that the point quasi-nucleus model makes it possible to find the values of energy levels with seven significant digits, taking into account the finite size of a quasi-nucleus in the first order of the perturbation theory yields eight significant digits in these values, and the quantum defect model ensures twelve significant digits.