Theory of Resonance Absorption Line Shapes in Monatomic Gases

Abstract

It is pointed out that the usual theories of pressure broadening disagree with direct experimental measurements of the widths of resonance-broadened alkali doublet lines, although the theories are at least qualitatively confirmed for the wings of resonance lines and for foreign-gas broadening. There are also two conflicting sets of experimental data (both in strong disagreement with theory). Some qualitative arguments are given for doubting the validity, near the center of a resonance line, of the "two-body" approximation generally used in theoretical treatments, and some formal objections to the usual procedure are also presented. The basic equation relating the susceptibility to a resolvent operator matrix element is derived from a more fundamental point of view than usual; the result contains in principle all effects due to translational motion, to the quantized nature of the radiation field, and to "spatial dispersion." In the limit of large absorber mass it is proved rigorously that the two-body approximation can never be valid near the center of a line, even for very low densities. By using different approximations for the wings and the line center, we obtain satisfactory agreement with experiments in both regions for the alkali doublet lines. We are also able to decide between the two conflicting experiments, favoring the square-root density dependence of the linewidth observed by Lauriston and Welsh.

Influence of Resonant and Foreign Gas Collisions on Line Shapes

“…The time between collisions is approximately given by [917r xb^v]" 1 where 91 is the perturber density. Thus, three-body collisions may be neglected if f 91 Tib 2 v] " 1 …”

Quantum‐Statistical Theories of the Cyclotron Resonance Lineshape in Parabolic Semiconductors

“…The fitness of equation (4.18) has been discussed by Kawamura et al, [4] in connection with their experiments. It may be noted that the square root density dependence has been also observed in the resonance absorption linewidth of monatomic gases [41].…”

Theory of Line Shapes

“…Then . Now (a) g n (t l9 t 2 ) =g(t 19 t$)g S (t l9 t:) 9 (b) 9 12 (t l9 1£) =g(t 19 t$)g S (t 19 ti), where a(t l9 *j) = (ifi) 2 Application of (A.38b) gives (5.2).…”

“…tin)' 1 * (l)ip + (2)^g <(1,2),(5.9) from whichg < (l, 2) results upon ensemble averaging. The time rate of change of the Heisenberg operator Q((t x ) is the Hamiltonian for the system.…”