FIZIKA A 9 (2000) 3 , 115-128

TWO-PHOTON TRANSITIONS IN HYDROGEN-LIKE ATOMS

MLADEN MARTINIS and MARKO STOJIĆ

R. Bosković Institute, P. O. Box 1016, HR-10001 Zagreb, Croatia

Received 11 October 1999; Accepted 25 January 2000

Different methods for evaluating two-photon transition amplitudes in hydrogen-like atoms are compared with the improved method of direct summation. Three separate contributions to the two-photon transition probabilities in hydrogen-like atoms are calculated. The first one coming from the summation over discrete intermediate states is performed up to n_c(max) = 35. The second contribution from the integration over the continuum states is performed numerically. The third contribution coming from the summation from n_c(max) to infinity is calculated in an approximate way using the mean level energy for this region. It is found that the choice of n_c(max) controls the numerical error in the calculations and can be used to increase the accuracy of the results much more efficiently than in other methods.

PACS numbers: 32.80.Cy
UDC 539.184

Keywords: two-photon transitions, hydrogen-like atoms, improved method of direct summation, transition probabilities, comparison with other methods

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