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Physical Review A

Effect of Time Ordering in the Unified Theory

J. T. Godfrey, C. R. Vidal, E. W. Smith, J. Cooper

Published May 1, 1971• 20 citations
Publisher

Abstract

Using a previously developed unified theory of spectral line broadening, the effects of time ordering over the complete line profile are investigated. The results of calculations for the Lyman-$\ensuremath{\alpha}$ line are presented.

DOI
10.1103/physreva.3.1543

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Using a previously developed unified theory of spectral line broadening, the effects of time ordering over the complete line profile are investigated. The results of calculations for the Lyman-\ensuremathα\ensuremath{\alpha}\ensuremathα line are presented.
Earlier calculations, based on customary radiation theory, fail to yield a meaningful finite answer for the second-order Stark effect upon line broadening. The reason for this occurrence is found in the assumption that, at some definite time, the radiating atom as well as the perturbing electron is in a precise energy state. When the electron is represented in a suitable way by a wave packet a finite line width results, and this answer agrees within reasonable limits with that of the classical impact theory provided certain enumerated conditions are satisfied.
The SSS matrices for Stark broadening of the n=1n=1n=1 and n=2n=2n=2 levels of hydrogen based on the straight-line classical-path model are calculated numerically. The interaction terms (excluding exchange) are included to all orders, and time ordering of the operators in the SSS matrix is retained. The resultant values for the impact-broadening operator $\ensuremath{\Phi}$ are presented. These results are compared with previous approximations based on the same model. The effect of the present calculations on the center and near wings of the Lyman-$\ensuremath{\alpha}$ line profile is considered.