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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Inelastic atomic collisions: generalization of Grawert parameters

E. Paul-Kwiek

Published Nov 18, 2003• 0 citations
Publisher

Abstract

The results of theoretical study of orientation, alignment and coherence effects in atomic collisions are presented. The conventional and coherence cross-sections that can be measured in collisional experiments with atomic beams are expressed via quantities dependent on the dynamics only and independent of geometry. The quantities introduced are the generalized Grawert parameters describing the collisional processes that occur in gas cell experiments (average cross-sections). The generalization of Grawert parameters allows us to obtian direct relationships between the average cross-sections and the conventional and coherence cross-sections.

DOI
10.1117/12.544379

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The results of theoretical study of orientation, alignment and coherence effects in atomic collisions are presented. The conventional and coherence cross-sections that can be measured in collisional experiments with atomic beams are expressed via quantities dependent on the dynamics only and independent of geometry. The quantities introduced are the generalized Grawert parameters describing the collisional processes that occur in gas cell experiments (average cross-sections). The generalization of Grawert parameters allows us to obtian direct relationships between the average cross-sections and the conventional and coherence cross-sections.
A formula has been obtained which describes the dependence of the overall cross section of the inelastic process in experiments with intersecting atomic and light beams on five parameters, two of which depend on the properties of the quasimolecule and the collisional energy, and three others on the degree of linear polarization of the exciting light and two angles which determine the geometry of the experiment. It was shown that measuring the overall cross section by varying the two latter parameters allows us to obtain additional information on the mechanism of the reactions. As an example, the experimentally studied process of spin transfer in Ca(4s5p/sup 1/P/sub 1/)+He and the process of Penning ionization of He(2/sup 1/P/sub 1/)+Cd(Zn) has been considered.
A general approximate method for computing the cross sections for certain inelastic collision processes is developed. It is based on the possibility of obtaining, with the use of the impact-parameter method, an exact expression for the transition amplitude in a special case. The dependence of the cross section on the parameters of coupling constant, velocity, and energy difference between states is discussed for a two-level model. Detailed calculations are made of cross section for collisions of the type $A(^{2}P_{\frac{3}{2}})+B\ensuremath{\rightleftharpoons}A(^{2}P_{\frac{1}{2}})+B$, where AAA is an excited atom of an alkali metal and BBB is an atom of a noble gas. An Appendix contains a review of the effective long-range interaction of atoms.
A two-level model of an atomic system is investigated in order to study the cross section for certain inelastic collision processes. An impact-parameter method is employed. The time-dependent Schr\"odinger equation has been integrated numerically for some simple interaction potentials. Cross sections for excitation have been determined and are presented as functions of the parameters describing the model. The results are compared with those obtained by certain approximate methods. The effects of inclusion of diagonal matrix elements in the interaction Hamiltonian are found to be large. For a fixed form of the interaction potential, two cross sections, which may differ quite substantially, are obtained, depending on the algebraic sign of the coupling parameters or the energy difference between the states.
A brief review is given on development of electron-photon coincidence studies from electron impact of atoms. The theory of electron-photon correlations is outlined in detail in terms of cross sections of excited atoms and excited state charge clouds. The state of a target atom is determined by the various orientation and alignment parameters and the multipole moments of the excited atom. General considerations, such as coherence effects in impact excitation, the influence of fine and hyperfine structures in correlations are taken into account. The relationship between scattering amplitudes (including their phases) and target parameters is worked out for singlet and doublet transitions.
A theoretical study of Stueckelberg interference structure in inelastic, state-changing integrated cross sections for collisions of low-Rydberg Na (n10) atoms with ground state He atoms is reported. The dependence of the Stueckelberg interference structure on orbital geometry and alignment of the initial state is predicted. Interference oscillations are found in the cross sections for both initial ns and np states; in the latter case, the features show considerable sensitivity with respect to variations in the spatial alignment of the principal axis of the electron charge distribution at some collision velocities and near isotropy at others.