Quantum scattering theory of rotational relaxation and spectral line shapes in H2–He gas mixtures

Abstract

A systematic study is presented of the rotational relaxation and spectral line shape properties of dilute gas mixtures of H2 in He, in an effort to determine the radial and angular dependence of the H2–He intermolecular potential. The quantum mechanical theory of relaxation in gases is reviewed, and we express the results in terms of a matrix of cross sections that determines each correlation function, and thus the relaxation properties of the system. The cross section is calculated from binary collision transition amplitudes, or S matrix elements, for H2–He scattering. A Morse-spline-fitted-van der Waals potential of the form V0(R)+V2(R)P2(cosθ) is assumed and we treat the hydrogen molecule as a rigid rotor. The Schrödinger equation is solved in the close-coupling approximation using the method of Gordon. We apply the theory to sound absorption measurements of rotational relaxation, NMR spin-lattice relaxation times, and the S and Q branches of the pure rotational Raman spectrum of H2–He mixtures. Elastic phase shift and reorientation effects are examined, along with the effects of energetically inelastic collisions. We find asymptotically closed channels to be unimportant, but the rigid rotor approximation breaks down in calculating the Raman line shifts due to the vibration-rotation interaction. This effect is accounted for by assuming different radial potentials V o(R) for scattering in two spectroscopic (vibrational) states. We find a potential that can accurately fit all the experimental data as well as the theoretical calculations of the long- and short-range behavior of the intermolecular potential.