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Physical Review A

Experimental determination of the density matrix describing collisionally produced H(n=3) atoms

C. C. Havener, Ned C. Rouze, W. B. Westerveld, and J. S. Risley

Published Jan 1, 1986• 50 citations
Publisher

Abstract

An experimental technique and analysis procedure is described for determining the axially symmetric density matrix for collisionally produced H(n=3) atoms by measuring the Stokes parameters which characterize the emitted Balmer-\ensuremath{\alpha} radiation as a function of axial and transverse electric fields applied in the collision cell. The electric fields induce strong characteristic variations in the Stokes parameters. The 14 independent elements of the density matrix are determined by fitting the observed Stokes parameters with signals calculated from a theoretical analysis of the experiment. The physical interpretation of the density matrix is presented in terms of graphs of the electron probability distribution and the electron current distribution. Examples of the determination of the density matrix are given for 40-, 60-, and 80-keV ${\mathrm{H}}^{+}$+He electron-transfer collisions.

DOI
10.1103/physreva.33.276

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Australian Journal of Physics•Apr 1, 1996•1 citation
An experimental technique and analysis procedure is described for determining the axially symmetric density matrix for collisionally produced H(n=3) atoms by measuring the Stokes parameters which characterize the emitted Balmer-\ensuremath{\alpha} radiation as a function of axial and transverse electric fields applied in the collision cell. The electric fields induce strong characteristic variations in the Stokes parameters. The 14 independent elements of the density matrix are determined by fitting the observed Stokes parameters with signals calculated from a theoretical analysis of the experiment. The physical interpretation of the density matrix is presented in terms of graphs of the electron probability distribution and the electron current distribution. Examples of the determination of the density matrix are given for 40-, 60-, and 80-keV H+{\mathrm{H}}^{+}H++He electron-transfer collisions.
Four signals characterizing the Balmer-alpha radiation resulting from 40-80-keV collisions of H+{\mathrm{H}}^{+}H+ on He were measured as a function of an applied transverse electric field. Detailed analysis allowed the axially symmetric density matrix of the H(n=3)\mathrm{H} (n=3)H(n=3) atom formed in the collision to be obtained. The imaginary parts of the off-diagonal density-matrix elements are presented as the distribution of the electronic current density in the atom. One of the first-order moments ${〈\stackrel{\ensuremath{\rightarrow}}{\mathrm{A}}\ifmmode\times\else\texttimes\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{L}}〉}_{z}^{s}$ of the current distribution is given.
In continuation of our previous work, charge transfer processes occurring in protons on rare-gas-atom collisions have been investigated. Diagonal and real off-diagonal coherence elements of the density matrix for H(n=3) atoms produced in 20--100-keV electron-capture collisions with Kr atoms are experimentally determined by analyzing the Balmer-\ensuremath{\alpha} light from the decay of H atoms from the (n=3) state to the (n=2) state. The intensity and polarization of the emitted light are measured as functions of an axially symmetric electric field in the collision region. These data are fitted to a numerical model of the H atom in an electric field in order to extract density-matrix elements. The results are compared to previous studies of H+{\mathrm{H}}^{+}H+ on He and Ar. The collisionally produced dipole moment of the H(n=3) atom decreases for increasing atomic number of the rare-gas target atoms, which indicates that the final phase of the collision process is not essential for the formation of the dipole moment. This physical picture is further supported by our alignment data. Absolute cross sections for charge transfer to the 3s, 3p, and 3d levels are presented as well.
Diagonal and real off-diagonal coherence elements of the density matrix for H(n=3) atoms produced in 20--100-keV electron-capture collisions of protons with Ar atoms are experimentally determined. Balmer-\ensuremath{\alpha} light from the decay of H atoms from the (n=3) state to the (n=2) state is observed. The intensity and polarization of the light as a function of an axially symmetric electric field in the collision region are fitted to a numerical model of the H atom in an electric field in order to extract density-matrix elements. A new polarimeter, using a photoelastic modulator in conjunction with photon-counting techniques, is used in the experiment, and its efficacy is analyzed and compared to that of a rotating quarter-wave plate polarimeter previously used in similar experiments. The diagonal elements of the density matrix yield relative capture cross sections for the H(3l) angular-momentum substates, while the coherence terms are used to determine the dipole moment of the atoms produced. Results are compared to those for protons colliding with a He target and the differences are discussed.
The branching ratios for the n=3 to n=2 Balmer-\ensuremath{\alpha} decay of hydrogen atoms in axial and transverse electric fields in the range 0--1000 V/cm have been calculated with use of a density-matrix formalism to take into account the time evolution of the atomic states in the presence of an electric field. The branching ratios are useful when the production of 2s hydrogen atoms is measured with the use of an electric field and when it is desired to correct for cascade contributions from the n=3 level. The total n=3 to n=2 branching ratio is found to depend on each of the 14 independent quantities which determine the axially symmetric n=3 density matrix, thus emphasizing the need to determine the complete density matrix including the off-diagonal coherence terms. If the off-diagonal density-matrix elements are not known, it is preferable to use transverse electric fields since, in this configuration, the contributions to the branching ratios from the off-diagonal terms are less than with axial electric fields. For transverse fields of approximately 200 V/cm, the contribution from the off-diagonal terms are nearly zero.
This paper is a theoretical discussion of a "coherence effect" in the excitation of hydrogen atoms to the n=3n=3n=3 state by electron bombardment. By coherence is meant that the density matrix describing the atom after the collision has off-diagonal matrix elements in the field-free basis. The differential cross section for producing Balmer-$\ensuremath{\alpha}$ photons at 90\ifmmode^\circ\else\textdegree\fi{} to the electron beam is calculated as a function of an applied longitudinal electric field. The off-diagonal elements show up as a dependence of the observed light on the directions of the electric field. Theoretical results based on the Born approximation are compared with an experiment at 200 and 500 eV. It is pointed out that this method for measuring relative phases of scattering amplitudes can be generally applied and is not restricted to n=3n=3n=3 excitation of hydrogen.
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.