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Physical Review A

Collisional coherent excitation to the n=2 state of hydrogen

Robert V. Krotkov, J. Stone

Published Aug 1, 1980• 26 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.22.473

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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-$\ensuremath{\alpha}$ 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.
We have measured Lyman-\ensuremath{\alpha} quantum beats from coherently excited hydrogen atoms produced in 85--235-keV proton collisions with a thin helium jet target. Intensity measurements of the radiation emitted at 90\ifmmode^\circ\else\textdegree\fi{} to the beam direction as a function of distance downstream from the target in electric fields both parallel and antiparallel to the beam axis allow extraction of the coherence between the s and p states by Eck's method [Phys. Rev. Lett. 31, 270 (1973)]. Because the jet target allows the collisions to occur in the applied field, we have eliminated the problems associated with field inhomogeneities when gas target cells are used. A strong-intensity peak emitted by excited helium in the target allows a determination of the starting point of the evolution in the field as well as a determination of the effects of experimental averaging. We present the s-p coherence parameters as a function of the projectile energy and compare them with recent theoretical calculations.
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 H+{\mathrm{H}}^{+}H+ impact are partly explained with the help of a simple model which assumes different cross sections for excitation into the different Stark states.
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.
This thesis presents the results of experimental investigation of coherence in the excitation of the 2p states of atomic hydrogen through a collision with an unpolarised electron. The polarisation correlation variation of the delayed coincidence method has been employed to simultaneously measure the reduced Stokes parameters P1,P2 and P3, which are needed to fully characterise the state of the atom immediately after the collision. This has also allowed the excitation coherence parameter P+ to be determined directly. In the case of the excitation of 2p states of hydrogen, a deviation of P+ from unity is indicative of the importance of spin exchange during the collision. A new Lyman- polarisation analyser, that permits independent rotation of a retarder and a linear polariser, was developed for this work. A novel approach to the analysis of data from electron-photon coincidence measurements has been implemented to improve the quality of the final results. The reduced Stokes parameters P1,P2 and P3 were measured at 54.4 eV electron energy, and in the 4-40 range of electron scattering angles. The P1 and P2 results are consistent with the earlier measurements, and recent theoretical predictions. The new P3 results, however, deviate significantly from the predictions of all modern theories, and also differ from previous experimental results. The newly measured values of P+ also suggest less coherent excitation than predicted by the theory, even at a relatively low scattering angle of 30. Several possible sources of systematic error including resonance radiation trapping, Stark mixing and erroneous phase-shift of the retarder have been considered, but are insufficient to explain the observed deviations from theory. Therefore, we are forced to conclude that spin exchange may play a more significant role during the collision than current theoretical methods predict.
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.