By using the general expression of the matrix elements of the transitions S1/2-P1/2, S1/2-P3/2, established in previous papers, and the Sommerfeld and Schur method of integration, the matrix elements of the transitions 1S1/2-continuum are carried out, in a first step, without retardation.

The general expressions with retardation of the matrix elements for a central potential of the transitions S1/2−P1/2 and S1/2−P3/2 have been established previously for all the cases of degeneracies. Here, they are calculated, for any Z, as combinations of hypergeometric series, for the transitions between 1S1/2 and the continuum (photoeffect). A verification of the results is achieved for the approximation Z2α2≪κ2 by using the integral representation in the complex plane of the confluent hypergeometric functions and the residues theorem.

The Einstein A coefficients are calculated, in all cases of degeneracies of the Dirac transition currents, by means of the energy balance method.

By using a geometrical form of the Darwin solutions of the Dirac equation, the general expressions with retardation of the matrix elements of the transitions S1/2-P1/2 and S1/2-P3/2 are established. The extension to the calculation with retardation of the sum rules relative to the intensities in the anomal Zeemann decomposition of the transitions between two levels is carried out.