Free-free matrix-elements for two-photon opacity

Abstract Recent opacity measurements have inspired a close study of the two-photon contributions to the opacity of hot plasmas. The absorption and emission of radiation is controlled by dipole matrix-elements of electrons in an atom or ion. This paper describes two independent methods to calculate matrix-elements needed for the two-photon opacity and tests the results by the f-sum rule. The usual f-sum rule is extended to a matrix f-sum that offers a rigorous test for bound-bound, bound-free and free-free transitions. An additional higher-order sum-rule for the two-photon transition amplitudes is described. We obtain a simple parametric representation of a key plasma density effect on the matrix-elements. The perturbation theory calculation of two-photon cross-sections is compared to an independent method based on the solution of the time-dependent Schroedinger equation for an atom or ion in a high-frequency electromagnetic field. This is described as a high frequency Stark effect or AC Stark effect. Two-photon cross sections calculated with the AC Stark code agree with perturbation theory to within about 5%. In addition to this cross check, the AC Stark code is well suited to evaluating important questions such as the variation of two-photon opacity for different elements. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U. S. Department of Energy or the United States Government.