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Physical Review Letters

Alignment and Orientation Effects in Beam-Foil Experiments

Y. B. Band

Published Nov 10, 1975• 17 citations
Publisher

Abstract

I present a theory of the orientation and alignment of atoms observed upon emergence from tilted foils. The interaction with the foil surface is taken into account in the production process of particular states. Once they are produced, the evolution of these states, under the influence of the residual field near the surface, is calculated in the fashion introduced by Eck. The most general effect of this evolution is presented.

DOI
10.1103/physrevlett.35.1272

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Physical Review A•Jan 1, 1987•6 citations
I present a theory of the orientation and alignment of atoms observed upon emergence from tilted foils. The interaction with the foil surface is taken into account in the production process of particular states. Once they are produced, the evolution of these states, under the influence of the residual field near the surface, is calculated in the fashion introduced by Eck. The most general effect of this evolution is presented.
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.
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 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.
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).
A simple model is presented in which the coherence between different mL{m}_{L}mL​ states in a tilted-foil, beam-foil experiment is induced by the electrostatic interaction between each beam particle and the foil as a whole. Agreement between the predictions of this model and the experimental results of Berry et al. seems sufficient to warrant refinement of the model and further experiments.
Theory for the generation and decay of high-lying Rydberg states in beam-foil experiments is presented. Our theory is designed to check the assumption that electron capture in the foil proceeds via a direct transition from a free state. The success of the theory in explaining the observed (primary and secondary) oscillatory structure and underlying smooth background of the ionization signal, as a function of additional variable electric fields, justifies this assumption. In addition, existence of asymmetry with respect to sign change of the variable fields is predicted to be detectable at high field values. Generation of Rydberg atoms in beam-foil experiments is shown to be a sensitive probe of the state distribution prepared during the beam's passage through the foil. Our theory substantiates the claim that Rydberg atoms produced in the beam-foil encounter exit the foil in a pure superposition state.