The method of matrix elements' calculations for the Dirac equation in the Coulomb field

Abstract

The method of matrix elements' calculations for the Dirac equation in the Coulomb field based on the virial relations is suggested. A matrix representation of virial relations for the Dirac equation in the Coulomb field is given. An explicit form of matrices in the cases of direct and inverse recursion is found. Possible applications of the suggested method are discussed and the probability of forbidden M1 transitions is calculated as an example.