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Physical Review A

Theory of alignment and orientation in beam-foil experiments

Y. B. Band

Published Jun 1, 1976• 41 citations
Publisher

Abstract

The preferential population of magnetic quantum levels of atomic states produced in beam-foil collisions is explained using a density-matrix formulation. The density matrix for the beam in the interior of the foil is evolved in time to obtain the density matrix after emergence from the foil. The dependence upon tilt angle of the foil relative to the beam is calculated. The Stokes parameters of the light emitted by decay of the atomic state are given in terms of the density matrix. Formulas which are valid for arbitrary angular momentum of the atomic state are derived. Comparison with experiment shows good agreement with data.

DOI
10.1103/physreva.13.2061

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Electronic state alignment, orientation, and coherence produced by beam-foil collisions

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The cylindrically symmetric beam-foil collision produces excitation and alignment of atom and ion levels similar, but not identical, to that resulting at comparable energies from ion-atom or ion-molecule collisions. When the foil is tilted, the macroscopic change acts on the microscopic scale to produce coherent alignment and orientation of the excited levels. The maximum beam energy range bounding this interaction has not yet been defined. The dynamic interaction which produces these effects is currently not predicted by any theory, although the dynamics of the ions subsequent to the collision are well understood. Refinement of current experimental technique can be expected to better define the final foil surface. The beam-tilted-foil collision promises to be useful in the study of ionic structure via quantum beat, radio-frequency and level-crossing spectroscopy techniques, and may provide a useful probe for certain surface interactions. 4 figs, 48 refs.

•Jul 22, 1975•0 citations
The preferential population of magnetic quantum levels of atomic states produced in beam-foil collisions is explained using a density-matrix formulation. The density matrix for the beam in the interior of the foil is evolved in time to obtain the density matrix after emergence from the foil. The dependence upon tilt angle of the foil relative to the beam is calculated. The Stokes parameters of the light emitted by decay of the atomic state are given in terms of the density matrix. Formulas which are valid for arbitrary angular momentum of the atomic state are derived. Comparison with experiment shows good agreement with data.
We investigate the validity of the surface electric-field interaction model in beam-foil experiments where the polarization of the emitted light is measured. After summarizing the theory for expanding the density operator into state multipoles and linking these to the Stokes parameters of the light, we show also how to use symmetries to reduce the size of the calculations. A very simple model is chosen for the electric field: it is perpendicular to the foil and constant over a finite distance, then zero. This model is used to find the initial density matrix for the n=3 singlet states of He i and the electric-field parameters from tilted-foil experiments. Reasonable results are obtained given the unrealistic electric-field model used.
The time evolution of alignment and orientation of excited atoms in an electric field is described using a density-matrix treatment. Orientation is produced by applying a tilted static electric field on levels aligned by beam-foil interaction. The modulation of polarization of the light is observed either inside the zone of constant field, by moving along the atomic beam, or downstream, in the field-free zone, by sweeping the field strength. Two different geometries are used for relative directions of ion beam, electric field vector, and foil normal. Tensor polarizabilities and cross sections for excitation of Zeeman sublevels are deduced from frequencies and amplitudes of quantum beat signals. Results are given for n 1{\mathrm{}}^{1}1D2{D}_{2}D2​ levels of 4i(n=3^{4}\phantom{\rule{0ex}{0ex}}\mathrm{i}\phantom{\rule{0ex}{0ex}}(\mathit{n}=34i(n=3, 4, and 5).
We have measured the polarization state of the light emitted in the 4He^{4}\mathrm{He}4He I, $2s^{1}S\ensuremath{-}3p^{1}P$ transition after excitation in a beam-foil experiment and find a partial elliptical polarization which depends upon the tilt angle of the carbon foil relative to the beam axis. This indicates that the emergent beam is oriented as well as aligned as a result of an interaction at the foil surface. The relative excitation cross sections and off-diagonal density-matrix elements have been deduced for the angular-momentum sublevels.
Polarization up to 15% has been detected in the decay of electronic levels in many-electron monatomic systems which were excited by the beam-foil method, the foil being tilted with its plane at 65\ifmmode^\circ\else\textdegree\fi{} to the particle velocity. Quantum beats were found even with an external magnetic field oriented parallel to the particle velocity, indicating that coherence is produced in the beam-foil interaction itself. Results are reported for various levels in He i, O ii, and Ar ii.
The cylindrically symmetric beam-foil collision produces excitation and alignment of atom and ion levels similar, but not identical, to that resulting at comparable energies from ion-atom or ion-molecule collisions. When the foil is tilted, the macroscopic change acts on the microscopic scale to produce coherent alignment and orientation of the excited levels. The maximum beam energy range bounding this interaction has not yet been defined. The dynamic interaction which produces these effects is currently not predicted by any theory, although the dynamics of the ions subsequent to the collision are well understood. Refinement of current experimental technique can be expected to better define the final foil surface. The beam-tilted-foil collision promises to be useful in the study of ionic structure via quantum beat, radio-frequency and level-crossing spectroscopy techniques, and may provide a useful probe for certain surface interactions. 4 figs, 48 refs.