A new approach is laid out to investigate two-photon atomic transitions. It is based on the application of the finite-basis solutions constructed from the Bernstein polynomial (B-polynomial) sets. We show that such an approach provides a very promising route for the relativistic second-order (and even higher-order) calculations since it allows for analytical evaluation of the involved matrices elements. In order to illustrate possible applications of the method and to verify its accuracy, detailed calculations are performed for the 2s1/2 → 1s1/2 transition in neutral hydrogen and hydrogen-like ions, which are compared with the theoretical predictions based on the well-established B-spline basis-set approach.
|Journal||Journal of Physics A: Mathematical and Theoretical|
|Publication status||Published - 17 Jun 2011|