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Journal of Physics B Atomic and Molecular Physics

Coherent excitation of hydrogen atoms by proton impact

O Schöller, J S Briggs, R. M. Dreizler

Published Aug 28, 1986• 44 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/19/16/010

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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.
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 collision of a proton with a hydrogen atom in the presence of electromagnetic radiation which is nearly resonant with the atomic levels is investigated theoretically. The non-perturbative quasi energy method is used to describe the laser-atom interaction and the proton-dressed atom collision is solved using a diagonalization technique. We have calculated the transition probabilities and the total cross-section for various transitions. We discuss the influence of various laser and collision parameters on the excitation process.
Two-photon ionisation of atomic hydrogen is considered in the non-relativistic dipole approximation at the photoelectric threshold and above it. In this region are obtained convergent analytical expressions for the radial transitions matrix elements, necessary for the calculation of ionisation rates. Partial and total cross sections per unit intensity are calculated for two-photon ionisation of atomic hydrogen in excited states with 2<or=n<or=9 by linearly and circularly polarised light at the photoelectric threshold and above it. At the photoelectric threshold calculations are also carried out for the two-photon ionisation of atomic hydrogen in the ground state.
This series of articles will describe a novel method of utilizing optical detection of RF-induced fine structure transitions to investigate the population of excited states of fast hydrogen atoms produced by charge exchange collisions between an initial proton beam and various gas or foil targets. In Part I a model of the charge exchange collision and the interaction of the hydrogen beam with an external oscillatory field are considered within the framework of the density matrix formalism and expressions are obtained for the RF lineshapes in terms of the initial atomic density matrix elements.
The profile of a hydrogen emission line is investigated on the assumption that the hydrogen atom is perturbed by passing ions. Provided that the ions do not approach to within ten times the average atomic radius the electric field of the ion may be assumed homogeneous and the matrix elements calculated for the usual Stark effect may be used. For a collision at low velocity or with close approach, the adiabatic approximation is valid, and the profile depends solely on the total phase shift produced by the collision. The Fourier analysis of the wave train may be carried through exactly for certain values of this phase shift. Nonadiabatic transitions are examined for the lowest lines, and an exact solution given for this case also. For higher lines a modified Born approximation is used. The Weisskopf collision broadening formula is shown to hold only in certain cases, and the dispersion curve smearing function for impact broadening is shown to lead in some instances to incorrect results.