- Access by Xinjiang University
Theory of Collision Broadening in the Sudden Approximation
Phys. Rev. 134, A625 – Published 4 May, 1964
DOI: https://doi.org/10.1103/PhysRev.134.A625
Abstract
A method is developed for calculating the cross section for line broadening in the limiting case in which important collisions may be considered to occur very rapidly with respect to the periods corresponding to the transitions in question. This method is essentially an extension of the familiar "sudden" approximation; reference is made throughout to the particular example of optical double resonance only for definiteness and because there are available experimental results for comparison with the theory. Assuming the impact model and considering the case when the energy levels in question are well resolved with respect to their width, an exact expression is found for resonant self-broadening in the usual weak rf field limit of interest in double resonance. For the case of very small oscillator strengths for the optical transition (intercombination lines), the resonant broadening becomes sufficiently small so that second-order, intermediate-state processes dominate, and approximations must be made to effect sums over intermediate states. Here the broadening is of the same sort as foreign gas broadening, and in many cases of interest, the approximations can be made in a sufficiently realistic manner to obtain useful expressions for the broadening. It is shown that the resonant cross section and this "second-order" cross section are not additive, but that the one which is larger dominates the total cross sections very strongly. Finally, we evaluate explicitly the self-broadening and foreign gas broadening (by the noble gases) of double resonance lines in the group II metals and the self-broadening in the optical spectrum of helium. In all cases our theoretical predictions are in good agreement with measurements which have been made.
References (19)
- M. Dumont, thèse de troisième cycle, Ecole Normale Sup. Paris, 1962 (unpublished)
- F. W. Byron, Jr., thesis, Columbia University, 1963 (unpublished)
- C. A. Piketty-Rives, diplôme d'études supérieures, Ecole Normale Sup. Paris, 1960 (unpublished)
- V. Furrsov and A. Vlassov, Physik Z. Sowjetunion 10, 378 (1938)
- R. G. Breene, Jr., The Shift and Shape of Spectral Lines (Pergamon Press, Inc., New York, 1961)
- E. Majorana, Nuovo Cimento 9, 43 (1930)
- J. Brossel and F. Bitter, Phys. Rev. 86, 308 (1952)
- C. J. Tsao and B. Curnette, Geophysical Research Paper No. 69, September 1960 AFCRL-TR60-278, Department of Commerce, Washington, D. C. (unpublished)
- P. W. Anderson, Phys. Rev. 76, 647 (1949)
- F. D. Colegrove, P. A. Franken, R. R. Lewis, and R. H. Sands, Phys. Rev. Letters 3, 420 (1959) P. A. Franken, Phys. Rev. 121, 508 (1961) M. E. Rose and R. L. Carovillano, 122, 1185 (1961)
- J. N. Dodd and G. W. Series, Proc. Roy. Soc. (London) A263, 353 (1961)
- J. P. Barrat, J. Phys. Radium 20, 541, 633, 657 (1959)
- H. M. Foley, Phys. Rev. 69, 616 (1946)
- E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, New York, 1957)
- A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, New Jersey, 1957)
- J. C. Slater, Phys. Rev. 36, 57 (1930)
- A. Lurio and A. Landman (private communication)
- L. S. Ornstein, J. P. A. van Hengstum, and H. Brinkman, Physica 5, 145 (1938) J. W. Schuttevaer and J. A. Smit, ibid. 10, 502 (1943) D. R. Bates and A. Damgaard, Phil. Trans. Proc. Roy. Soc. London A242, 101 (1950)
- H. Kuhn and W. Vaughan (to be published)