Solving quasi-relativistic equations for hydrogen-like ions with account of the finite size of a nucleus

Quasi-relativistic equations for hydrogen-like ions are investigated. In solving them, the finite size of a nucleus is taken into account. The contact interaction with a nucleus is taken into consideration while solving the quasi-relativistic equations for all electrons, not only the s-ones. The single-electron energies and the averaged distances from the origin obtained are compared to the data of relativistic calculations and of a widely known computer program by R. Cowan.