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Physical Review A

Connection between the bremsstrahlung tip and direct radiative recombination: Angular distributions and polarization correlations

I.J. Feng, Ira B. Goldberg, Young Soon Kim, Richard H. Pratt

Published Aug 1, 1983• 16 citations
Publisher

Abstract

We illustrate the possibility for calculation of bremsstrahlung tip angular destributions and polarization correlations from corresponding photoeffect results with an extension of the method for connecting bremsstrahlung tip and direct-radiative-recombination (DRR) cross sections developed by Lee and Pratt. The agreement between results obtained with this method and results from our numerical partial-wave calculations is, in general, satisfactory. We note features of the distributions and correlations, and once again point out the inadequacies of the nonrelativistic dipole approximation for the evaluation of bremsstrahlung or DRR angular distributions.

DOI
10.1103/physreva.28.609

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We illustrate the possibility for calculation of bremsstrahlung tip angular destributions and polarization correlations from corresponding photoeffect results with an extension of the method for connecting bremsstrahlung tip and direct-radiative-recombination (DRR) cross sections developed by Lee and Pratt. The agreement between results obtained with this method and results from our numerical partial-wave calculations is, in general, satisfactory. We note features of the distributions and correlations, and once again point out the inadequacies of the nonrelativistic dipole approximation for the evaluation of bremsstrahlung or DRR angular distributions.
Using exact analytical expressions of the nonrelativistic dipole recombination cross sections for a pure Coulomb potential summed over the quantum numbers j and l, we numerically compute the recombination cross sections in the various n states for 1\ensuremath{\le}n\ensuremath{\le}500 and the total cross section for all possible values of the incoming electron energy. We present a parametrization of the recombination cross sections in the various n states, of the total cross section, and of the energy emission cross section. A few low- and high-energy approximations are also derived and discussed.
Total and differential two-photon ionization cross sections are derived in the framework of perturbation theory, assuming a simple one-electron atomic model. It is shown that for an unpolarized target the angular distribution of the ejected electrons has the general form $\mathrm{a}+b{cos}^{2}\ensuremath{\theta}+c{cos}^{4}\ensuremath{\theta}$, whatever the quantum numbers nnn, lll, of the initial energy level, and the state of polarization (linear or circular) of the incident radiation. The total transition rates for circularly and for linearly polarized light are quite different from each other. For an arbitrary nl\mathrm{nl}nl state, the theoretically allowed maximum value of their ratio is 32\frac{3}{2}23​. Further analytical and numerical results are presented for hydrogen. The Appendix contains several useful summation formulas for spherical harmonics.
The method for calculating the function of angular photon correlation and the angular distribution of photons emitted in the process of dielectronics recombination at any phase of a cascade of radiative and Auger transitions was presented. This method was developed incorporating the formalism of the spin density matrix and the kinetic Pauli equation as the basis. The calculations conducted revealed that the effect of alignment transfer in a cascade can have a strong impact on the shape of angular correlation of cascade photons.
A method alternative to the density matrix formalism is applied to derive a general expression for the radiative decay probability following the photoionization of polarized atoms in two-step approximation. The graphical technique of the angular momentum theory is used for the integration over angular and spin variables. The general expression joining both steps of photoionization and fluorescence contains the possibility to investigate the polarization of all particles in the initial and final states and the angular distributions as well as angular correlations of photoelectrons and radiation. A simple way to get the expressions for special cases of the angular distribution and polarization of fluorescence radiation in the photoionization of randomly orientated and polarized atoms is given as an example of the practical application of the general formula.
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.
The angular distribution and polarization of the resonance radiation are deduced for elliptically polar- ized light incident on an atomic system of arbitrary initial and intermediate total angular momenta. The incident and re-radiated light are characterized by Stokes's representation, which allows an immediate generalization to partially polarized incident radiation. The results follow closely in form those deduced for free electron (Rayleigh) scattering but give, in general, a rather smaller degree of anisotropy for the resonance radiation. The results also determine the complete correlation, in polarization and direction of propagation, of two successive quanta emitted by a radiating system