The Use of Wigner Expansion and Path Integral Method for Quantum Correction of the Low-Order Spectral Moments and Collision-Induced Absorption Profiles

Abstract

This study aims at examination of the lower-order spectral moments in collision-induced absorption (CIA), taking the translational He-Ar band as an example. General quantum corrections for the zeroth and first spectral moments are derived on the basis of the Wigner expansion up to the order of $\hbar^8$ and $\hbar^{10}$, respectively. These corrections were then explored for numerical simulation of the He-Ar moments over the temperature range 50-500 K. The accuracy of the obtained temperature dependencies is validated through the comparison with direct quantum solution of the scattering and bound-state problems as well as with the results obtained using the path integral (PI) approach. Quite satisfactory agreement was achieved as a result of the application of the two independent ways of approximate accounting for the quantum nature of absorption. The robustness of the Wigner expansion and PI corrections was thus demonstrated, both of which can be used to obviate direct quantum simulation of the CIA spectral moments. The approximate method is suggested for an accurate simulation of the CIA spectral profile on the basis of the obtained quantum-corrected moments and the classical trajectory-based formalism.