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Physical Review A

Zeros in (inverse) bremsstrahlung matrix elements

C. David Shaffer, Richard H. Pratt, Sung Dahm Oh

Published Jan 1, 1998• 3 citations
Publisher

Abstract

We discuss the possibility of zeros in the nonrelativistic radiative continuum-continuum matrix element for electron-atom (inverse) bremsstrahlung. As demonstrated earlier for upward transitions from bound states, the occurrence of different signs for the free-free matrix element in limiting cases, plus the requirement of continuity, implies the existence of zeros. Using knowledge of the sign of the dipole matrix element in the soft- and hard-photon limits with one continuum electron energy held fixed, we show that zeros can occur in the $s$-$p$ matrix element. We discuss the connection of our results to elastic scattering and to Ramsauer-Townsend minima. We consider the observability of zeros in this $(s$-$p)$ matrix element manifested as minima in the cross sections.

DOI
10.1103/physreva.57.227

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Minima in cross sections (Cooper minima) are known to occur for all types of transitions in atoms. These minima are caused by zeros in the transition matrix elements which are the result of a zero value for the radial integral of a particular energy. These minima can occur in both the bound-bound and bound-free transition matrix elements. In this paper the approximate position (energy) of the zeros in the bound-bound quadrupole and octupole matrix elements of the point Coulomb field are presented. The positions are found to change in the same manner as those found in the continuum, even to the extent that a zero first occurring in a bound-bound matrix element will move into the corresponding bound-free matrix element.
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We report the results of new theoretical calculations of the transition amplitudes and cross-sections for two distinct bremsstrahlung-related processes : i) Stimulated one-photon transitions (Free-Free Transitions) occuning in the course of electron-H atom collisions, in the presence of a strong extemal field. ii) Two-photon Bremsstrahlung, corresponding to the spontaneous emission of two distinct photons in a single electron-atom collision event. The main features of these processes will be outlined and discussed.
By use of the linear-response-vectors method, the Kramers-Heisenberg matrix elements for arbitrary bound-bound transitions of a nonrelativistic hydrogenlike atom have been evaluated. To illustrate the discussion, Rayleigh and Raman scattering have been selected as relevant examples of second-order processes. We have derived, in a unitary manner, A- and \ensuremath{\varphi}-gauge compact analytic formulas, both for angular momentum and Stark states. Our results are expressed in terms of two new generalized hypergeometric functions with four variables, 1FE_{1}\mathrm{F}_{\mathrm{E}}1​FE​ and 2FE_{2}\mathrm{F}_{\mathrm{E}}2​FE​, which are finite sums of Gauss hypergeometric functions. Special attention is given to the two-photon transitions involving the atomic ground state. For angular momentum states, we mention the connection that we have established between our general results and earlier ones.
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