Quantum number and energy scaling for nonreactive collisions

Abstract

Two new theoretical developments are presented in this article. First an energy corrected sudden (ECS) approximation is derived by explicitly incorporating both the internal energy level spacing and the finite collision duration into the sudden S-matrix. An application of this ECS approximation to the calculation of rotationally inelastic cross sections is shown to yield accurate results for the H+–CN system. Second, a quantum number and energy scaling relationship for nonreactive S-matrix elements is derived based on the ECS method. A few detailed illustrations are presented and scaling predictions are compared to exact results for R–T, V–T, and V–R, T processes in various atom–molecule systems. The agreement is uniformly very good — even when the sudden approximation is inaccurate. An important result occurs in the analysis of V–T processes: the effects of anharmonic wave functions (coupling) and decreasing vibrational energy gaps (energetics) are separated. Each factor makes significant contributions to the deviation of the anharmonic from the harmonic scaling relationship.

Energy corrected sudden calculations of linewidths and line shapes based on coupled states cross sections: The test case of CO2–argon

“…It may be seen that including the extrapolated values has removed the artificial falloff in the CS-ECS results at high ͉m͉. The two different models of the adiabaticity factor give substantially different results, and the factor of Bonamy et al 25 gives better agreement with experiment and with direct calculations than that of De Pristo et al 10 This corroborates the previous analysis based on the N 2 -N 2 case, 25 and in the remainder of this paper we will consider only results obtained with the ''Bonamy'' factor. The extrapolated CS-ECS predictions are also in good agreement with the experimental results for the normalized near wing absorption, as shown in Fig.…”

“…The resulting model, designated the extrapolated CS-ECS procedure, performs well for high-pressure band profiles ͑up to 1000 atm͒ and for near-wing absorption as well as for linewidths. The adiabaticity factor recently proposed by Bonamy et al 25 appears to perform better than that of De Pristo et al 10 Finally, the CS basic rates have been used to evaluate the accuracy of the empirical basic rates Q L Ј(T) obtained previously from an optimization procedure based on a simple analytical law.…”

“…The ECS approach introduces ''adiabaticity factors'' ⍀ J which approximately correct for the changes in kinetic energy and the finite duration of collisions. 10 Two possible choices for the adiabaticity factors will be discussed below. Two different ECS formalisms have been proposed for line shape calculations.…”

“…Accordingly, parametric models of the relaxation matrix are often employed, ranging from very simple models to sophisticated schemes such as the energycorrected sudden ͑ECS͒ approximation. 1 The ECS approach 10 includes the angular momentum coupling needed to handle interbranch mixing, and expresses the relaxation matrix ͑for an atomic perturber͒ in terms of a set of so-called ''basic rates'' Q L Ј(T), which are actually thermally averaged inelastic cross sections for downwards transitions to the ground state, 0 (L→0,T). In the past, the basic rates have usually been modeled through some simple analytical expression, such as the exponential power ͑EP͒ law, 11…”

ROBO: a model and a code for studying the interstellar medium

“…To this aim, we may adopt the steady-state equations of McKee et al (1982) and the rates calculated by Schinke et al (1985) by applying the L → 0 coefficients to the Goldflam et al (1977) method and including the Depristo et al (1979) correction (see these studies for more details).…”