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Physical Review Letters

Spin-Dependent Orientation Propensities Revealed in Polarized-Electron–Polarized-Photon Coincidence Studies

N. Andersen, Klaus Bartschat, John T. Broad, G F Hanne, M. Uhrig

Published Jan 8, 1996• 24 citations
Publisher

Abstract

The density matrix parametrization of collisionally excited atomic ensembles is generalized to account for a projectile spin. The elements are related to the ``generalized Stokes parameters'' of Andersen and Bartschat [J. Phys. B 27, 3189 (1994)], determined in scattered-projectile--polarized-photon coincidence experiments after impact excitation by spin-polarized electrons. The well-established orientation propensity rule for unpolarized electron beam experiments is not valid for spin-resolved collisions.

DOI
10.1103/physrevlett.76.208

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The density matrix parametrization of collisionally excited atomic ensembles is generalized to account for a projectile spin. The elements are related to the ``generalized Stokes parameters'' of Andersen and Bartschat [J. Phys. B 27, 3189 (1994)], determined in scattered-projectile--polarized-photon coincidence experiments after impact excitation by spin-polarized electrons. The well-established orientation propensity rule for unpolarized electron beam experiments is not valid for spin-resolved collisions.
The density matrix parametrisation of collisionally excited atomic ensembles is generalised to account for projectile and target spin polarisations. The density matrix elements, containing spin-resolved alignment and orientation parameters, can be determined by measurements of the 'generalised Stokes parameters' introduced by Andersen and Bartschat (1994) to describe scattered-projectile-polarised-photon coincidence experiments. Focusing on electron impact excitation of light alkali-type targets and mercury, the present experimental status of such experiments is reviewed, in particular with regard to the 'perfect scattering experiment' whereby all independent scattering amplitudes are determined.
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.
For a quantum system, the density matrix contains all the statistical information that can be obtained from measurements. For excited atomic states, the coefficients in a spherical basis expansion of the density matrix, up to rank two, are proportional to Alignment and Orientation Parameters given by Fano and Macek and are called the state multipoles or multipole moments. They can be experimentally determined from the measurements of the Stokes parameters of the emitted photon. To obtain maximum possible information, one needs to break the axial symmetry of the experiment by specifying a reflection plane determined through a coincidence measurement. For LS coupled atomic states, if one can spectroscopically resolve J-multiplets, and if the process is spin dependent, information about the contributions to the state multipoles due to orbital and spin angular momenta can be extracted. In the process, it is also possible to determine the octupole moments of the excited state due to orbital and spin angular momenta. An illustrative example from transfer-excitation reactions in He+-Ar collisions at low keV energies will be presented. For coupling schemes other than LS coupling, using a similar decoupling one can determine the contributions due to appropriate angular momenta. The method is general enough that one can apply it to ion, atom, electron or photon projectiles incident on atomic targets.
Electron-photon coincidences with initially polarized electrons have been measured for the first time. Results for linear and circular polarization components of the 254-nm line (Hg $6^{3}P_{1}\ensuremath{-}6^{1}S_{0}$ transition) are presented as a function of electron energy for electrons which are scattered inelastically (63P16^{3}P_{1}63P1​ excitation) in the forward direction. The analysis of these polarization components allows one to determine the role of spin-dependent interactions during collision as well as to determine the relative phase of the two scattering amplitudes involved.
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.
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.