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Physical Review Letters

Coherence Measurement of Tensor Multipoles of Asymmetrically Excited Atomic States

D. A. Church, M. C. Michel, William F. Kolbe

Published May 5, 1975• 8 citations
Publisher

Abstract

A specific coherence measurement technique is described, which yields the relative magnitudes of all predicted orientation and alignment parameters in tilted-foil-excited levels of ions and atoms. Quantum-beat frequencies and relative magnitudes are measured as a function of applied magnetic field strength and direction, and analyzed using Fano-Macek theory. The multipole moments of tilted-foil-excited 40-keV $^{4}\mathrm{He}$ $4d^{1}D_{2}$ atoms are measured and related to proposed excitation mechanisms.

DOI
10.1103/physrevlett.34.1140

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Physical Review Letters•Oct 21, 1974•21 citations
A specific coherence measurement technique is described, which yields the relative magnitudes of all predicted orientation and alignment parameters in tilted-foil-excited levels of ions and atoms. Quantum-beat frequencies and relative magnitudes are measured as a function of applied magnetic field strength and direction, and analyzed using Fano-Macek theory. The multipole moments of tilted-foil-excited 40-keV 4He^{4}\mathrm{He}4He 4d1D24d^{1}D_{2}4d1D2​ atoms are measured and related to proposed excitation mechanisms.
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 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).
The intensity of beam-foil-excited $\mathrm{Ly}\ensuremath{-}\ensuremath{\alpha}$ radiation has been measured in electric fields alternately parallel and antiparallel to the beam. Measurements were made at three energies---110, 165, and 210 keV---and three field strengths. From these data the $S\ensuremath{-}P$ co-herence term ${\ensuremath{\sigma}}_{\mathrm{SP}}$ has been determined. The magnitude of ${\ensuremath{\sigma}}_{\mathrm{SP}}$ is found to be 0.07 at 110 keV, 0.19 at 160 keV, and 0.22 at 210 keV. These results establish that beam-foil-excited hydrogen atoms have a nonzero electric dipole moment.
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.
We excited helium atoms using 10--20-keV H2+{\mathrm{H}}_{2}^{+}H2+​ (D2+{\mathrm{D}}_{2}^{+}D2+​) ion impact and investigated the intensity of the \ensuremath{\lambda}(43{4}^{3}43D-23{2}^{3}23P)=447 nm line as a function of an electric field -2 kV/cm\ensuremath{\lesssim}F\ensuremath{\le}+2 kV/cm applied antiparallel and parallel to the ion beam. The recorded signals were strongly asymmetric with respect to the sign of the electric field. This asymmetry is explained by assuming a coherent excitation of He levels with different angular momenta (4d,4f and 5f,5g). These measurements demonstrate that angular momentum coherences of impact-excited states can also be observed in nonhydrogenic systems.
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.