Abstract
By using the plane-wave expansion for the electromagnetic-field vector potential, relativistic bound–bound, bound–unbound and unbound–unbound transition matrix elements for hydrogenic atoms are expressed universally in terms of hypergeometric functions. By applying the obtained formulas, these transition matrix elements can be evaluated analytically and numerically with arbitrarily high precision. The newfound representation for the matrix elements is very convenient for direct numerical evaluation of the Lamb shift because of its universality, conciseness and reliance on functions already built in the standard computational packages. All of this is highly favorable for programming of computationally efficient algorithms.
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