Molecular collisions, effect on the HD infrared spectrum and development of a Moyal quantum mechanical description
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Date
1997-11-01T00:00:00Z
Authors
McQuarrie, Barry Robert
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Abstract
Interference is possible between the allowed dipole moment of the molecule HD and the pair dipole moment induced by collision with a foreign gas atom. The resulting line shape can be described by the sum of a Lorentzian and an asymmetric profile. The mixing of rotational levels by an anisotropic interaction potential call permit components of the induced dipole moment that do not have the same symmetry of the allowed moment to interfere with it. For the rotational spectrum of HD-He and HD-Ar the effect of each component of the induced dipole moment on the line shape parameters is determined for various temperatures and transitions. For line intensity, the component with the same symmetry as the allowed moment always dominates, but the effect of the other components is shown to be significant. The line shape parameters for the vibrorotational spectrum of HD-He are calculated for $P\sb1(1),\ R\sb1(0),\ R\sb1(1)$ transitions at 77, 195, and 295 K. Moyal quantum mechanics is an alternative to Heisenberg or Schrodinger quantum mechanics. The method yields a semiclassical expansion of phase space trajectories in terms of Planck's constant, h. The Moyal correction to the classical part of the solution is found to $O(h\sp2)$. The first computational version of Moyal quantum mechanics to calculate average values for three dimensional systems with physically relevant parameters is developed. The system treated is the scattering of a Gaussian wave packet by the helium, neon, and argon interaction potentials. The Gaussian is squeezed in momentum so that the momentum average an be done analytically. This introduces a momentum correction and the Gaussian is taken to have a single initial velocity. We examine scattering at velocities of 300-1200 m/s. Sensitive areas of the phase space average are identified. Integrals over coordinate phase space (impact parameter and displacement y) are examined in detail. The region of phase space which produces rainbow scattering is determined to result in the largest quantum effects. The Moyal correction is found to be small for impact parameters greater than $2b\sb{rainbow} - b\sb{glory}$. The corrections to average values are examined in detail for helium at a velocity of 300 m/s. It is shown that the Moyal corrections have an asymptotic time behaviour which is the same as that of the classical part of the average, but that they may grow as $t \to \infty$ to dominate the total average. The corrections to the average value are examined as functions of mass and velocity. The Moyal correction is seen to change sign relative to the classical part of the average in both cases. The momentum correction is shown to have a mass$\sp{-2}$ dependence. More complex asymptotic behaviour of the Moyal correction is examined for both the mass and the velocity. Comparison between the size of the correction for the systems consisting of two helium, neon, and argon atoms is performed. (Abstract shortened by UMI.)