Gauge invariance and approximate multiphoton calculations in hydrogen

Yves Justum, Alfred Maquet, and Y. Heno
Phys. Rev. A 41, 2791 – Published 1 March 1990
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Abstract

It has been observed that fairly accurate estimates for two-photon bound-bound amplitudes in hydrogen can be obtained from a simple partial summation restricted to the discrete spectrum contribution, provided one uses the E⋅r form of the interaction Hamiltonian. We show that this conclusion does not hold when considering higher-order multiphoton processes. In fact, the corresponding multiple sums can be shown to be divergent and, consequently, no reliable estimates can be obtained from such an approximation. Using the (1/c)A⋅p form of the interaction does not lead to reliable estimates either. Those conclusions are based on a comparison with exact results for the second- and fourth-order contributions to the ac Stark shift of the ground state, computed with the help of a Sturmian basis.

  • Received 28 September 1989

DOI:https://doi.org/10.1103/PhysRevA.41.2791

©1990 American Physical Society

Authors & Affiliations

Yves Justum

  • Laboratoire de Chimie Théorique, Université de Paris–Sud, F-91405 Orsay, France

Alfred Maquet

  • Joint Institute for Laboratory Astrophysics, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309-0440

Y. Heno

  • Laboratoire de Chimie Physique, Université Pierre et Marie Curie, 11 Rue Pierre et Marie Curie, F-75231 Paris CEDEX 05, France

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Issue

Vol. 41, Iss. 5 — March 1990

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