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Physical Review Letters

Anisotropy in the Beam-Foil Light Source

H. G. Berry, L. J. Curtis, David G. Ellis, Richard M. Schectman

Published Apr 8, 1974• 139 citations
Publisher

Abstract

We have measured the polarization state of the light emitted in the $^{4}\mathrm{He}$ 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.

DOI
10.1103/physrevlett.32.751

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Physical Review A•Sep 1, 1986•4 citations
We have measured the polarization state of the light emitted in the 4He^{4}\mathrm{He}4He I, 2s1S\ensuremath−3p1P2s^{1}S\ensuremath{-}3p^{1}P2s1S\ensuremath−3p1P 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 measurements have been made as a function of foil-tilt angle for the He I transitions $2s^{3}S\ensuremath{-}3p^{3}P^{o}(3889 \AA{})$ and $2p^{3}P^{o}\ensuremath{-}4d^{3}D(4471 \AA{})$. Particular attention was paid to the systematic effects that can enter into the analysis of such data from the decreasing time resolution as the foil-tilt angle is increased. It is shown that particle scattering at the foil is the main source of systematic error, but that this error can be eliminated by appropriate analytic techniques. The forms of the variation of the relative Stokes parameters with tilt angle are found to be very similar to those previously found for the corresponding singlet transitions, although the magnitudes of the alignment and orientation parameters are generally different for the singlets from the values we find for the triplets. The present results for 3p3Po3p^{3}P^{o}3p3Po are shown to be reasonably consistent with those recently published by Burns et al., provided that the necessary correction for decreasing time resolution at high tilt angles is included.
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.
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 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).