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Zeitschrift für Naturforschung A

Calculation of Line Broadening Cross Sections for Level Crossing Experiments in Alkali-Rare Gas Systems

Bernd Grosswendt

Published Apr 1, 1974• 0 citations
Publisher

Abstract

Using a simple approximation for the theoretical atomic interaction constants cross section data for level crossing and Hanle-effect line broadening experiments in Rb, Mg+ and Ca+ rare gas systems could be derived. It is shown that in the Rb system the interaction C6R-6 is predominant and that the results are little influenced by dipole-quadrupole and repulsive interactions in the frame work of the Lindholm-Foley-Hindmarsh theory.

DOI
10.1515/zna-1974-0409

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Using a simple approximation for the theoretical atomic interaction constants cross section data for level crossing and Hanle-effect line broadening experiments in Rb, Mg+ and Ca+ rare gas systems could be derived. It is shown that in the Rb system the interaction C6R-6 is predominant and that the results are little influenced by dipole-quadrupole and repulsive interactions in the frame work of the Lindholm-Foley-Hindmarsh theory.
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The author obtains expressions for Rydberg level broadening and shift cross sections and rates suitable for elastic collisions of ground-state rare-gas atoms with Rydberg atoms. The semiclassical impact broadening theory is used. The interaction of a Rydberg atom with a rare-gas atom is approximated by the superposition of polarisation potentials and the Fermi pseudopotential. It is shown that similar expressions for the broadening and shift cross sections due to the perturber-Rydberg-electron interaction can be obtained in the JWKB approximation for the Rydberg-electron wavefunctions and for the square-well model potential. Consequently the shift and width of the Rydberg level are not very sensitive to the shape of the potential but only to its normalisation. Expressions for the shift and width in the square-well potential approximation suitable in the high-density limit of the perturbing atoms are obtained. Limits of the applicability of the expressions for the broadening and shift cross sections are discussed. Calculated broadening and shift rates agree well with experimental results for the broadening and shift of Rydberg levels with small, medium and large principal quantum numbers by all rare gases excepting neon.
The theory of impact broadening of the isolated spectral lines of the Rydberg atomic series perturbed by neutral particles is developed within the framework of the impulse approximation. The analysis of the broadening process is based on the consideration of the inelastic nl to n' transitions between highly excited states of the Rydberg atom. The role of the potential and resonance scattering of the quasifree electron by a perturbing particle in the impact broadening of the Rydberg nl levels is investigated. It is shown that the general expressions for the broadening cross sections presented in this paper contain the results of asymptotic Alekseev and Sobel'man theory (1965) as special cases. Both elastic and inelastic scattering contributions of the perturber by the parent core of Rydberg atom to the broadening cross sections are also considered within the framework of the 'shake' model. The results obtained are used for a quantitative explanation of experimental data on the broadening of Rydberg atomic levels perturbed by alkali-metal atoms. The energies and widths of the 3 P resonances on the quasidiscrete levels of the negative K - and Rb - ions are determined.
The purpose of this work is the evaluation of the linewidth w and lineshift d of the sodium resonance line 3p − → 3s when the excited atoms are evolving in their parent gas. Assuming the Baranger impact approximation, these two quantities are given in terms of the phase shifts of the ground Na(3s) + Na(3s) and the excited Na(3p)+Na(3s) states. The quantal calculations and the semi-classical method, developed by Mott and Massey and Landau and Lifshitz, show that the cross sections σ and λ vary with the energy like E−1/2, the width w and the shift d do not depend on the temperature, the long-range interactions have a big influence on w and d, and the rate coefficients depend on the dispersion coefficients like w/n ≈ +7.298 × 10−8C3(Σ) and d/n ≈ +8.893 × 10−9C3(Σ). The study also shows that the sodium results can be extended to the other alkali-metal atoms (Li, K, Rb, Cs, and Fr) by a simple scaling. Keywords: potential energy curve, broadening cross section, rate coefficient, linewidth, lineshift, dispersion coefficient