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Journal of Physics B Atomic Molecular and Optical Physics

P-state-to-P-state transitions in optically prepared atomic collisions: I. Theory of measurement in terms of Stokes parameters

Emil Y. Sidky, Sonia Grego, D. Dowek, N. Andersen

Published Apr 24, 2002• 6 citations
Publisher

Abstract

We present a parametrization in terms of Stokes parameters for the scattering from a P state to a P state for atomic collisions in a beam experiment. The classic approach to a `complete scattering experiment', well known for S-state-to-P-state transitions, is generalized by a systematic combination of optical preparation of specific initial P states with Stokes parameter analysis of the radiation pattern from the final P state. The anisotropy of the initial and final state provides the possibility of extraction of a complete set of nine parameters describing the reaction at the level of five independent scattering amplitudes. We discuss the minimum number of experiments required to obtain a complete set of parameters in the cases of scattering angle-integrated and scattering angle-differential measurements. Relations to collision parameters for the reverse process are derived. Finally, effects due to fine and hyperfine depolarization, as well as inclusion of electron spin polarization, are treated.

DOI
10.1088/0953-4075/35/9/302

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We present a parametrization in terms of Stokes parameters for the scattering from a P state to a P state for atomic collisions in a beam experiment. The classic approach to a `complete scattering experiment', well known for S-state-to-P-state transitions, is generalized by a systematic combination of optical preparation of specific initial P states with Stokes parameter analysis of the radiation pattern from the final P state. The anisotropy of the initial and final state provides the possibility of extraction of a complete set of nine parameters describing the reaction at the level of five independent scattering amplitudes. We discuss the minimum number of experiments required to obtain a complete set of parameters in the cases of scattering angle-integrated and scattering angle-differential measurements. Relations to collision parameters for the reverse process are derived. Finally, effects due to fine and hyperfine depolarization, as well as inclusion of electron spin polarization, are treated.
Electron scattering by excited sodium atoms has been carried out in a crossed-beam experiment. The atoms have been optically pumped into a well defined hyperfine level (3 2 P 3 2/F=3) by a tunable CW dye laser. For two of the most prominent scattering processes, the 3 2 P to 3 2 S and 3 2 P to 4 2 S transitions, the effect of the anisotropy of the initial state introduced by the laser light is studied in detail and is interpreted in terms of multipole moments describing the optical excitation and the collision process. Possibilities and limitations of the experiment are discussed. Electron collisions may be seen as a test case for the understanding of more involved interaction processes.
An experimental investigation of electron - impact induced transitions from the laser - excited 3P state of sodium atom to the 4S and 3D excited states is presented, the main objective being measurement of the atomic collision parameters ( ACPs ) that are related to individual scattering amplitudes. These parameters are complementary to the differential excitation cross - sections and provide finer details on the collisional excitation process. The experiment involved the preparation of the 3P - state with coherent laser radiation of a particular polarisation and measuring the rate of electrons scattered from the laser - excited state as function of laser polarisations. The ACPs were then deduced from these measurements and optical pumping parameters, which account for the optical preparation of the 3P - state. To formulate different measurement schemes, a measurement theory based on the general description of transitions between states of different angular momentum using density matrix formalism is derived. The investigation of the 3P - 4S transition is very similar to the studies of the 3S - 3P excitation performed by superelastic method involving the 3P - 3S scattering in the 'time - inverse' geometry. 'Standard' ACPs are used and, similarly to the superelastic method, the measurements for the 3P - 4S excitation performed in the 'time - inverse' geometry also reveal ACPs for the 4S - 3P de -excitation process. For the more complex 3P - 3D transition, however, the 'standard' ACPs may be less informative. It is shown that certain sums of individual magnetic sublevel excitation probabilities can be measured which may be considered as atomic collision parameters for transitions between P and D - states.
The description of alignment and orientation for collisional excitation of atomic states by electron and heavy-particle impact, including electron transfer processes, is reviewed. For D states, a new parametrization of the excited atomic ensemble is proposed, and the density matrices describing the excited target state and the light emitted in a subsequent optical decay are expressed in terms of the new parameter set. Recipes for performing complete experiments through scattered-particle - multiple-photon coincidence set-ups are discussed. Because of the difficulties associated with such experiments, attention is also given to the generally incomplete case of scattered-particle - one-photon coincidence arrangements. For D-state excitation, it is demonstrated how the new set of parameters allows for a systematic description of the collision process, and provides opportunities for consistency checks.
An overview is given of the present understanding of excitation in electron–atom collisions, with particular emphasis on the extent to which a "perfect scattering experiment" in the Bederson sense has been achieved. Recent experimental and theoretical results are put into a common framework, generalizing the ideas and systematics, presented in a review paper, of the case of excitation by spin-polarized electron beams. For various levels of complexity, complete sets of coherence parameters are suggested, and their relationships to generalized Stokes parameters and generalized STU parameters are pointed out.
Collisions studies using optically state selected beams is discussed. Measurements of spin resolved differential cross sections for superelastic scattering of electrons from excited sodium atoms (3P) are reported. The excited states are prepared by laser optical pumping with circularly polarized light thus giving a pure atomic state before the collision. A crossed beam arrangement of sodium atoms and electrons is used with a scattered electron detector. Scattered electron intensity as a function of scattering angle, incident electron energy, and relative orientation of the incident electronic and atomic spins is measured. 8 refs., 10 figs.
Recent data from two methods in which high resolution laser radiation is used to assist in determining electron-atom collision parameters are presented. The electron superelastic method has yielded the first measurement of Stokes parameters for electron de-excitation of the 32D5/2–32P3/2,1/2 transition of atomic Na, the upper level having been optically prepared by resonant, stepwise excitation from the 32S1/2 ground level via the 32P3/2 level using two single mode lasers. As well, we report on the development of a model to determine the optical pumping parameters for superelastic scattering from the 32P3/2 level when it is prepared by two lasers exciting from the F = 1 and F = 2 states respectively of the 32S1/ 2 ground level. Data are also presented for collision parameters for the excitation of the 61So–61 PI transition of the I = 0 isotope of Hg by electrons of 50 eV incident energy. The technique employed for these measurements is the stepwise electron–laser excitation coincidence method, in which the electron excited atom is further excited by resonant laser radiation, and fluorescence photons emitted by relaxation from the laser excited state are detected in coincidence with the scattered electron.