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Physical Review A

Coherent excitation of the n=3 states in hydrogen

Robert V. Krotkov

Published Nov 1, 1975• 19 citations
Publisher

Abstract

This paper is a theoretical discussion of a "coherence effect" in the excitation of hydrogen atoms to the $n=3$ 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 $n=3$ excitation of hydrogen.

DOI
10.1103/physreva.12.1793

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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-\ensuremathα\ensuremath{\alpha}\ensuremathα 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.
In a measurement of emission of Balmer-$\ensuremath{\alpha}$ flux from atomic hydrogen or deuterium excited by electron impact in a crossed-beam experiment, a longitudinal electric field which enhances the Balmer-$\ensuremath{\alpha}$ flux by Stark-mixing components of like MJ{M}_{J}MJ​ within the n=3n=3n=3 shell, does so asymmetrically depending on whether the field is applied parallel or antiparallel to the electron beam. The effect is attributed to coherent excitation of states of opposite parity.
This paper presents measurements of the Lyman-$\ensuremath{\alpha}$ photons emitted when target gases He, Ar, O2{\mathrm{O}}_{2}O2​, and N2{\mathrm{N}}_{2}N2​ are bombarded by a beam of ground-state hydrogen atoms. The collisions take place in the presence of an axial electric field and the observed Lyman-$\ensuremath{\alpha}$ brightness depends on field direction. This observation is interpreted as evidence for excitation of hydrogen atoms to states which are linear superpositions of 2s2s2s and 2p2p2p. Measurements are presented of a "mixed" cross section ${\ensuremath{\sigma}}_{\mathrm{sp}}$ which characterizes the degree of coherent excitation. The real part of ${\ensuremath{\sigma}}_{\mathrm{sp}}$ measures the electric dipole moment created by the collision, while the imaginary part measures the rate at which the moment is changing. It is found that these quantities vary substantially over the energy range 3-30 keV, with maximal values being about as large as permitted theoretically. Coherent excitation should be present to some degree in all inelastic collisions and, when measurable, provides new tests of scattering theory. Some implications are also discussed for precision frequency measurements and searches for weak-interaction effects in atomic physics.
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.
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.
The density matrix describing excitation of the n=2 and n=3 levels of atomic hydrogen under proton impact is calculated, both in the first Born approximation and in a close-coupling expansion in target eigenstates. Various ways in which the properties of the excited state can be characterized in terms of certain linear combinations of density matrix elements are discussed. A new characterisation, based on an extrapolation below threshold of parameters describing the angular distribution of low-velocity ionised electrons, is suggested.
We consider electron scattering by hydrogen atoms in a bichromatic linearly polarized laser field of frequencies ω and 3ω and we discuss the coherent control of the scattering process as a function of the relative phase φ between the two components of the radiation field. The electrons are assumed to have sufficiently high energies in order to permit the description of the scattering process in the first-order Born approximation. The scattered electrons, embedded in the bichromatic laser field of moderate power, as well as the laser dressing of the hydrogen atoms in their ground state are described by time-dependent perturbation theory. We discuss the angular dependence of the nonlinear differential scattering cross sections for the low values N = ±2 of absorbed or emitted laser photons as a function of the relative phase φ between the two radiation field components. We also compare our results with those obtained from the assumption of a static potential describing the target atom.