Abstract
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.
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Boudet, R., Blaive, B. Exact Relativistic Calculation with Retardation of the Matrix Elements Used in the Photoeffect of Hydrogenic Atoms. Foundations of Physics 30, 1283–1300 (2000). https://doi.org/10.1023/A:1003688522459
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DOI: https://doi.org/10.1023/A:1003688522459