Infinite order sudden approximation for rotational energy transfer in gaseous mixtures

Abstract

Rotational energy transfer in gaseous mixtures has been considered within the framework of the infinite order sudden (IOS) approximation. A new derivation of the IOS from the coupled states Lippmann–Schwinger equation is given. This approach shows the relation between the IOS and CS T matrices and also shows in a rather transparent fashion Secrest’s result that the IOS method does not truncate closed channels but rather employs a closure relation to sum over all rotor states. The general CS effective cross section formula for relaxation processes is used, along with the IOS approximation to the CS T matrix, to derive the general IOS effective cross section. It is then observed that this cross section can be factored into a finite sum of ’’spectroscopic coefficients’’ Fn(j′aj′b‖jajb ‖L) and ’’dynamical coefficients’’ QL(k). The Fn(j′aJ′b‖jajb ‖L) can be calculated once and tabulated since they do not depend at all on the particular system considered. The QL(k) can be shown to equal the integral inelastic cross section for the transition j=0 to j=L, so that if these cross sections are evaluated, either theoretically or experimentally, other types of cross sections can be computed without any further dynamical calculations. In principle, the factorization permits one to calculate other types of cross sections if any one type of cross section has been obtained by some procedure. The functional form can also be used to compact data. This formalism has been applied to calculate pressure broadening for the systems HD–He, HCl–He, CO–He, HCN–He, HCl–Ar, and CO2–Ar. In order to test the IOS approximation, comparisons have been made to the CS results, which are known to be accurate for all these systems, as well as to several exact close coupling, semiclassical, and experimental values for some of the systems. The IOS approximation is found to be very accurate whenever the rotor spacings are small compared to the kinetic energy, provided closed channels do not play too great a role. For the systems CO–He, HCN–He, and CO2–Ar, these conditions are well satisfied and the IOS is found to yield results accurate to within 10%–15%.