Cluster Expansion of Relaxation Function and Its Application to the Theory of Pressure Broadening

Abstract

The time relaxation function for pressure broadening is derived in the cumulant expansion form with the number densities of the system as variates. In this derivation the multiple collisions are taken into account and the Boltzmann distribution is assumed. By introducing the Born-Oppenheimer approximation and the statistical approximation, each cumulant can be written as a sum of irreducible integrals. When there is no correlation between perturbers and their effect on the absorber is scalarly additive, all cumulants drop out except the binary collision term. The criterion for the validity of the statistical approximation is that the rate of time change of difference between adiabatic potentials of initial and final states to this difference is much smaller than the frequency deviation from the natural frequency. The reason why the Jablonski’s quantum mechanical theory gives the equivalent result with that by the classical method of Kuhn-London is clarified.