Abstract
The methods of kinetic theory are used to describe the radiation from an atom immersed in a gas of perturbing particles. It is shown that the line shape can be expressed in terms of a one-particle distribution function. The appropriate BBGKY hierarchy of equations is derived. This hierarchy is then truncated by assuming that only two-body collisions are important. The resulting equations are solved to obtain a non-Markovian kinetic equation which describes the combined effects of Doppler and pressure broadening. When the Markovian assumption is applied, a generalized linear Boltzmann equation is obtained which describes the line shape in the region where the impact limit is valid and which also describes the phenomenon of collisional narrowing.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Popielawski and S. A. Rice,J. Chem. Phys. 47:2292 (1967).
E. W. Smith and C. F. Hooper, Jr.,Phys. Rev. 157:126 (1967).
U. Fano,Phys. Rev. 131:259 (1963).
R. Zwanzig,J. Chem. Phys. 33:1338 (1960).
B. Bezzerides,Phys. Rev. 181:379 (1969).
N. N. Bogoliubov, inStudies in Statistical Mechanics, I. J. deBoer and G. E. Uhlenbeck, eds., North-Holland Publishing Co., Amsterdam (1962), Vol. I.
J. P. Wittke and R. H. Dicke,Phys. Rev. 103:620 (1956).
S. G. Rautian and I.I. Sobel'man,Soviet Phys.-JETP 9:701 (1967).
J. M. J. Van Leeuwen and S. Yip,Phys. Rev. 139:A1138 (1965).
J. P. Dougherty and D. T. Farley, Jr.,J. Geophys. Res. 68:5473 (1963).
E. G. Pestov and S. G. Rautian,Soviet Phys.-JETP 29:488 (1969).
E. W. Smith, J. Cooper, W. R. Chappell, and T. Dillon,J.Q.S.R.T., in publication.
W. E. Brittin and W. R. Chappell,Rev. Mod. Phys. 34:620 (1962).
I. Prigogine,Non-Equilibrium Statistical Mechanics, Interscience Publishers, New York (1962).
E. W. Smith, C. R. Vidal, and J. Cooper,J. Res. Natl. Bur. Std. U.S. 73A:389, 405 (1969).
J. Weinstock,Phys. Rev. 132:454 (1963).
R. Balescu,Statistical Mechanics of Charged Particles, Interscience Publishers, New York (1963).
N. Rostoker,Phys. Fluids 7:479, 491 (1964).
K. Huang,Statistical Mechanics, John Wiley and Sons, New York, (1963), p. 132.
P. L. Bhatnagar, E. P. Gross, and M. Krook,Phys. Rev. 94:511 (1954).
Author information
Authors and Affiliations
Additional information
This research was supported in part by the Advanced Research Projects Agency of the Department of Defense, monitored by Army Research Office-Durham under Contract No. DA-31-124-ARO-D-139.
Rights and permissions
About this article
Cite this article
Chappell, W.R., Cooper, J., Smith, E.W. et al. A kinetic theory of spectral line shapes. J Stat Phys 3, 401–410 (1971). https://doi.org/10.1007/BF01008278
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01008278