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Journal of Physics B Atomic and Molecular Physics

Even-odd parity coherence effects in electron-hydrogen scattering

Karl Blum, Hans Kleinpoppen

Published Nov 11, 1977• 17 citations
Publisher

Abstract

The angular distribution and polarisation of hydrogenic line radiation excited by electron impact is considered for the case of coincidence experiments. The theory of coherent excitation of hydrogenic states with opposite parity is developed. A set of multipole parameters is defined which characterise the excited states and which enable the formulation of Fano and Macek to be generalised.

DOI
10.1088/0022-3700/10/16/022

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The angular distribution and polarisation of hydrogenic line radiation excited by electron impact is considered for the case of coincidence experiments. The theory of coherent excitation of hydrogenic states with opposite parity is developed. A set of multipole parameters is defined which characterise the excited states and which enable the formulation of Fano and Macek to be generalised.
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.
A determination of all the state multipoles of the n=2 excited state of atomic hydrogen has been made. The kinematical conditions were a crossed electron-atom-beam geometry in which the incident electron energy was 350 eV and the scattering angle 3'. The experimental technique measures the scattered 10.2 eV energy loss electrons in coincidence with the 10.2 eV photons from either the 2P state or the delayed Stark-quenched 2S-state decay. An external electrostatic field mixes the S and P states, permitting the observation of their coherence by measuring the linear and circular photon polarisations, while in-plane angular correlations for a zero electric field determine the P-state multipoles. The state multipoles were deduced from a least-squares fit of the measured data to the quantum mechanical expressions determined for a model of an S-P (m j =1/2) superposition excited state with averages over the singlet and triplet spin states.
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.
Abstract The dipole radiation emitted by an atom excited by a unidirectional electron beam has a nonuniform angular distribution which is simply related to the percentage polarization P of the radiation emitted perpendicular to the beam. P was first calculated using the OppenheimerPenney (O.-P.) theory. In this theory the probability of excitation of an upper quantum state and the probability of subsequent emission of a polarized photon from such a state are considered independently. P is finally expressed in terms of the cross-sections QM for excitation of states of definite component of angular momentum along the direction of the electron beam. In general, P is dependent on detailed numerical calculations of QM j, but the selection rule A = 0 removes this dependence at threshold. In the O.-P. theory allowance may be made for fine structure and hyperfine structure, but the theory is ambiguous when the f.s. or h.f.s. separations are comparable with the line width. A theory is therefore developed which is based on the calculation of the probability of a polarized photon being emitted by the complete system of atom + electron. The ambiguity of the O.-P. theory is removed by integration over line profiles, but the expressions reduce to O.-P. expressions when the f.s. or h.f.s. separations are much smaller or much larger than the line width. The Lyot line of hydrogen is an intermediate case for which the line widths and the h.f.s. separations are comparable. Assuming the validity of the Born approximation, a simple expression is obtained which allows the QM to be calculated from the angular distribution of the scattered electrons. Theoretical predictions are compared with experimental results. For the Na£) lines the predicted polarization is small enough to escape experimental detection. Polarizations observed by - Skinner & Appleyard in 1927 for various Hg lines rise to maxima with decreasing electron energy, and then tend to values close to zero at threshold. These experimental results at low energies appear to be inexplicable in terms of the reactions considered, but if the polarization curve above the maximum is extrapolated to threshold, the theory and experiment are found to be in reasonable agreement. Further experimental work is thought to be desirable
A brief review is given on development of electron-photon coincidence studies from electron impact of atoms. The theory of electron-photon correlations is outlined in detail in terms of cross sections of excited atoms and excited state charge clouds. The state of a target atom is determined by the various orientation and alignment parameters and the multipole moments of the excited atom. General considerations, such as coherence effects in impact excitation, the influence of fine and hyperfine structures in correlations are taken into account. The relationship between scattering amplitudes (including their phases) and target parameters is worked out for singlet and doublet transitions.