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Physical Review A

Experimental determination of the real elements of the density matrix of H(n=3) atoms produced in 20–100-keV collisions of H+ on Kr

Norbert Seifert, N. D. Gibson, John S. Risley

Published Nov 1, 1995• 4 citations
Publisher

Abstract

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 ${\mathrm{H}}^{+}$ 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.

DOI
10.1103/physreva.52.3816

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Physical Review A•Dec 1, 1997•4 citations
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.
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.
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.
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 key features of the cross sections for electron-impact excitation out of the ground levels of the rare-gas atoms are summarized and application of these cross section data is shown. This is followed by discussions of recent experiments on determination of electron-impact cross sections for excitation out of the metastable levels of He and Ar. The metastiable atom targets are produced by two different methods, i.e., hollow-cathode discharges and charge-exchange collisions of rare-gas ions with Cs atoms. The former method is simple but is limited to low electron energies because of the very small metastable concentration, whereas the latter method yields a fast target beam with predominantly metastable atoms allowing measurements up to the keV range. The measured cross sections show features very different from those of excitation out of the ground levels. Another new development in electron-atom collision is the use of atom traps for measuring ionization cross sections. The experiment is conducted by passing an electron beam pulse through magneto-optically trapped Rb atoms while the trap is momentarily turned off. Turning the trap back on immediately after the electron beam pulse recaptures the unionized atoms allowing only the ions to escape. The ionization cross section is determined bymore » measuring the electron beam current density at the trapped atom region and the fractional loss of trapped atoms due to the electron beam. This method avoids measurements of the absolute number of the target atoms and the overlap between the atomic and electron beams and therefore eliminates the major sources of uncertainty associated with the crossed-beam method for measuring ionization cross section.« less
We have developed an experimental method for determining the initial density matrix of the foil-excited atoms. The excited hydrogen (n=2)(n=2)(n=2) atoms pass through a region of a variable electric field ($\ensuremath{-}200\mathrm{k}\mathrm{V}/\mathrm{m}$ to +200kV/m+200\mathrm{k}\mathrm{V}/\mathrm{m}+200kV/m), and the intensity of the Lyman-\ensuremath{\alpha} line (121.6 nm) emitted in a free space downstream is observed. By using a vacuum ultraviolet polarizer, the dependence of the intensities of the polarized components on the electric field, including the field-dependent quantum beats, was measured and it was numerically fitted to a calculation. Thus all the initial density matrix elements were determined in a single measurement. It was found that, in the energy range 100--180 keV, just after the excitation, the electron cloud has higher density in the front side of the ion and the electron probability current is backwards.