Physical Review A

Experimental determination of real elements of the density matrix and the dipole moment of H(n=3) atoms produced from 20–100-keV H+ on Ar

S. P. Renwick, E. C. Martell, W. D. Weaver, John S. Risley

Published Oct 1, 1993• 8 citations

Abstract

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.

DOI: 10.1103/physreva.48.2910

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Physical Review A

Experimental determination of real elements of the density matrix and the dipole moment of H(n=3) atoms produced from 20–100-keV H+ on Ar

S. P. Renwick, E. C. Martell, W. D. Weaver, John S. Risley

Published Oct 1, 1993• 8 citations

Publisher

Abstract

DOI: 10.1103/physreva.48.2910

Related papers

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

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.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.

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Physical Review AJan 1, 198650 citations

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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.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.

Physical Review ANov 1, 197519 citations

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R. Hippler, O. Plotzke, Wolfgang Harbich +3 more

Electric dipole moments of H(n=2) induced in ${\mathrm{H}}^{+\mathrm{\ensuremath{-}}}$He and H-He collisions are investigated at incident energies of 5--25 keV. For these collision systems, an energy-dependent forward-backward asymmetry (dipole moment) of the emitted Lyman-\ensuremath{\alpha} radiation as a function of an external electric field is observed. In ${\mathrm{H}}^{+\mathrm{\ensuremath{-}}}$He collisions, the measured dipole moment is positive, corresponding to an electron trailing behind the proton. The same analysis applied to the H-He system shows the electron riding in front of the proton. The observed differences between H and ${\mathrm{H}}^{+}$ impact are partly explained with the help of a simple model which assumes different cross sections for excitation into the different Stark states.Electric dipole moments of H(n=2) induced in ${\mathrm{H}}^{+\mathrm{\ensuremath{-}}}$He and H-He collisions are investigated at incident energies of 5--25 keV. For these collision systems, an energy-dependent forward-backward asymmetry (dipole moment) of the emitted Lyman-\ensuremath{\alpha} radiation as a function of an external electric field is observed. In ${\mathrm{H}}^{+\mathrm{\ensuremath{-}}}$He collisions, the measured dipole moment is positive, corresponding to an electron trailing behind the proton. The same analysis applied to the H-He system shows the electron riding in front of the proton. The observed differences between H and ${\mathrm{H}}^{+}$ impact are partly explained with the help of a simple model which assumes different cross sections for excitation into the different Stark states.

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Collisional coherent excitation to the n=2 state of hydrogen

Robert V. Krotkov, J. Stone

This paper presents measurements of the Lyman-$\ensuremath{\alpha}$ photons emitted when target gases He, Ar, ${\mathrm{O}}_{2}$ , and ${\mathrm{N}}_{2}$ 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 $2s$ and $2p$ . 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.This paper presents measurements of the Lyman-$\ensuremath{\alpha}$ photons emitted when target gases He, Ar, ${\mathrm{O}}_{2}$, and ${\mathrm{N}}_{2}$ 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 $2s$ and $2p$. 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.

Physical Review AAug 1, 198026 citations

{\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.

Four signals characterizing the Balmer-alpha radiation resulting from 40-80-keV collisions of

{\mathrm{H}}^{+}

on He were measured as a function of an applied transverse electric field. Detailed analysis allowed the axially symmetric density matrix of the

\mathrm{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.

{\mathrm{H}}^{+}

+He electron-transfer collisions.

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.

{\mathrm{H}}^{+}

impact are partly explained with the help of a simple model which assumes different cross sections for excitation into the different Stark states.

This paper presents measurements of the Lyman-$\ensuremath{\alpha}$ photons emitted when target gases He, Ar,

{\mathrm{O}}_{2}

, and

{\mathrm{N}}_{2}

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

2s

and

2p

. 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.