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Journal of Physics B Atomic and Molecular Physics

Optical electric resonance investigation of a fast hydrogen beam. I. Theory of the atom-RF field interaction

Mark P. Silverman, F. M. Pipkin

Published Apr 21, 1974• 7 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/7/6/013

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Coherent excitation of the n=3 states in hydrogen

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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.

Physical Review A•Nov 1, 1975•19 citations
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 lineshape theory of optically detected RF-induced electric resonance transitions in hydrogen is concluded with the treatment of the detection process within the framework of the density matrix formalism. An optical detection function is derived from which can be determined the intensity, polarisation, and angular distribution of the detected decay radiation, subject to constraints of apparatus efficiency and geometry, in terms of the initial atomic density matrix elements and variables of the radiofrequency electric field.
For pt.II, see ibid., vol.7, no.6, 730 (1974). The apparatus and experimental procedure for optical electric resonance investigation of a fast hydrogen beam are described. Particular attention is paid to the design and performance of the radiofrequency system. The generalized rotating field model of the atom-RF field interaction developed in Part I and the optical detection function derived in Part II are employed in conjunction with computer simulation and least squares fitting techniques to extract information on the initial states from experimental optical electric resonance spectra of the H(n=4) manifold.
The resonant interaction between an rf electric field and a coherent atomic state is studied by monitoring the field-induced changes in the quantum beats after a beam-foil collision. A theory for the interaction is discussed and a preliminary measurement of the fine-structure interval J=32J=\frac{3}{2}J=23​ to J=52J=\frac{5}{2}J=25​ in the n=4n=4n=4 state of hydrogen is presented.
Hydrogen atoms are excited into high Rydberg states following fast proton impact on a thin carbon foil. The effects of various electromagnetic fields on these atoms are observed by measuring the integral ionization yield in an additional constant electric field. These experiments reveal oscillations in that yield, regularly spaced as a function of electric field. A model is outlined that quantitatively describes the observed field dependence. This new phenomenon indicates selective excitation of the Stark substates.
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.