QED calculation of E1M1 and E1E2 transition probabilities in one-electron ions with arbitrary nuclear charge

The quantum electrodynamical theory of the two-photon transitions in hydrogenlike ions is presented. The emission probability for 2s(1/2) -> 2y(E1) + 1s(1/2) transitions is calculated and compared to the results of the previous calculations. The emission probabilities 2p(1/2) -> y(E1) + y(E2) + 1s(1/2) and 2p(1/2) -> y (E1) + y (M1) + 1s(1/2) are also calculated for the nuclear charge Z values 1 <= Z <= 100. This is the first calculation of the two latter probabilities. The results are given in two different gauges.