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Physical Review A

Branching ratios for the decay ofn=3hydrogen atoms in axial and transverse electric fields

Ned C. Rouze, C. C. Havener, W. B. Westerveld, and J. S. Risley

Published Jan 1, 1986• 5 citations
Publisher

Abstract

The branching ratios for the n=3 to n=2 Balmer-\ensuremath{\alpha} decay of hydrogen atoms in axial and transverse electric fields in the range 0--1000 V/cm have been calculated with use of a density-matrix formalism to take into account the time evolution of the atomic states in the presence of an electric field. The branching ratios are useful when the production of 2s hydrogen atoms is measured with the use of an electric field and when it is desired to correct for cascade contributions from the n=3 level. The total n=3 to n=2 branching ratio is found to depend on each of the 14 independent quantities which determine the axially symmetric n=3 density matrix, thus emphasizing the need to determine the complete density matrix including the off-diagonal coherence terms. If the off-diagonal density-matrix elements are not known, it is preferable to use transverse electric fields since, in this configuration, the contributions to the branching ratios from the off-diagonal terms are less than with axial electric fields. For transverse fields of approximately 200 V/cm, the contribution from the off-diagonal terms are nearly zero.

DOI
10.1103/physreva.33.294

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The branching ratios for the n=3 to n=2 Balmer-\ensuremath{\alpha} decay of hydrogen atoms in axial and transverse electric fields in the range 0--1000 V/cm have been calculated with use of a density-matrix formalism to take into account the time evolution of the atomic states in the presence of an electric field. The branching ratios are useful when the production of 2s hydrogen atoms is measured with the use of an electric field and when it is desired to correct for cascade contributions from the n=3 level. The total n=3 to n=2 branching ratio is found to depend on each of the 14 independent quantities which determine the axially symmetric n=3 density matrix, thus emphasizing the need to determine the complete density matrix including the off-diagonal coherence terms. If the off-diagonal density-matrix elements are not known, it is preferable to use transverse electric fields since, in this configuration, the contributions to the branching ratios from the off-diagonal terms are less than with axial electric fields. For transverse fields of approximately 200 V/cm, the contribution from the off-diagonal terms are nearly zero.
The branching ratios for radiative decay of H atoms excited in small electric fields (0--5 V/cm) have been calculated for the nl states up to n=6. A simple computational procedure was employed, allowing only for Stark-effect mixing of levels with the same values of the quantum numbers (n,j,mj{m}_{j}mj​). The results are compared with more detailed calculations available for 3l-state decay made using the density-matrix formalism, and new calculations of this type reported here for 4l-state decay. In conjunction with theory, this allowed the domain of validity of the simple computational procedure to be established as a function of n. The results show that the branching ratios depend quite strongly on electric-field magnitude, pointing to the need to exercise caution in measurements of H emissions, and in application of the available data to other problems.
An experimental technique and analysis procedure is described for determining the axially symmetric density matrix for collisionally produced H(n=3) atoms by measuring the Stokes parameters which characterize the emitted Balmer-\ensuremath{\alpha} radiation as a function of axial and transverse electric fields applied in the collision cell. The electric fields induce strong characteristic variations in the Stokes parameters. The 14 independent elements of the density matrix are determined by fitting the observed Stokes parameters with signals calculated from a theoretical analysis of the experiment. The physical interpretation of the density matrix is presented in terms of graphs of the electron probability distribution and the electron current distribution. Examples of the determination of the density matrix are given for 40-, 60-, and 80-keV H+{\mathrm{H}}^{+}H++He electron-transfer collisions.
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.
Four signals characterizing the Balmer-alpha radiation resulting from 40-80-keV collisions of H+{\mathrm{H}}^{+}H+ on He were measured as a function of an applied transverse electric field. Detailed analysis allowed the axially symmetric density matrix of the H(n=3)\mathrm{H} (n=3)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.
The probabilities of two-photon decay for hydrogen (H) and antihydrogen ( Hˉ \bar H Hˉ ) atoms in the presence and absence of an external electric field are analytically calculated. In particular, the probabilities of the E1E2 and E1M1 transitions between the 2p and 1s levels are calculated for the case when emitted photons are characterized by polarization vectors and wavevectors. It is shown that, in an external electric field, the decay probabilities for 2s and 2p levels differ for H and Hˉ \bar H Hˉ atoms because of interference terms linear in field. Coulomb Green’s function method is used for summing over intermediate states.
Four experiments involving individual and combined effects of electric fields and multiple exciter foils on beam-foil-excited hydrogen atoms are described.The use of multiple exciter foils shows that excitation equilibrium does not occur in the thin carbon foils used here. The change of the rate of decay of Ly-α flux emitted by beam-foil excited hydrogen atoms in an electric field has been used to determine the relative populations of the 2s and 2p levels at the foil. The 2s level is overpopulated with respect to the 2p level when one foil is used and two exciter foils enhance the overpopulations. Photoelectric measurements of Ly-α flux and photographic measurements of the decay of Balmer-δ flux emitted by atoms in an electric field show that quasiperiodic intensity variations exist on the decay curve. The variations are attributed to the effect of the electric field but discrepancies arise between the experimental frequencies and those calculated from Stark-effect theory.