Increasing interest in multiphoton absorption processes above the ionization threshold has led theorists to reexamine numerical techniques for calculating radiative transition matrix elements between states of a continuum electron moving at large radial distances in the field of an atom or an ion. Here it is shown that accurate free—free radial matrix elements may be obtained using the usual dipole length formula by means of a rotation at finite distance in the complex coordinate plane together with solution of the free-electron wave function's phase and amplitude at finite distance in the complex coordinate plane. The procedure is designed for use with numerically calculated wave functions for many electron atoms and ions. It avoids the use of analytic asymptotic formulas as well as transformation to the dipole acceleration formula and is accurate even for matrix elements between electron stales that are close in energy, which is the case for which the alternative integration-by-parts method is inaccurate. We present comparisons of our numerical procedure with both analytic results and results of the integration-by-parts procedure for the case of free—free electron transitions in a pure Coulomb field.
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Research Article|
November 01 1987
Numerical methods for free—free radiative transition matrix elements
Bo Gao;
Bo Gao
Department of Physics and Astronomy, The University of Nebraska, Lincoln, Nebraska 68588-0111
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Anthony F. Starace
Anthony F. Starace
Department of Physics and Astronomy, The University of Nebraska, Lincoln, Nebraska 68588-0111
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Bo Gao
Anthony F. Starace
Department of Physics and Astronomy, The University of Nebraska, Lincoln, Nebraska 68588-0111
Comput. Phys. 1, 70–73 (1987)
Article history
Received:
July 20 1987
Accepted:
August 19 1987
Citation
Bo Gao, Anthony F. Starace; Numerical methods for free—free radiative transition matrix elements. Comput. Phys. 1 November 1987; 1 (1): 70–73. https://doi.org/10.1063/1.4903436
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