1. The Classification of Exact Quantum Methods for Nonreactive Scattering. 2. Quantum Mechanical Calculations of Rotational-Vibrational Scattering in Homonuclear Diatom-Atom Collisions. 3. The Effect of the Potential Well on Vibrational Scattering and the Validity of SSH Theory

Citation

Wagner, Albert Fordyce (1972) 1. The Classification of Exact Quantum Methods for Nonreactive Scattering. 2. Quantum Mechanical Calculations of Rotational-Vibrational Scattering in Homonuclear Diatom-Atom Collisions. 3. The Effect of the Potential Well on Vibrational Scattering and the Validity of SSH Theory. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/wtpc-sy44. https://resolver.caltech.edu/CaltechTHESIS:12042017-113526294

Abstract

Part 1. The exact quantum methods for the cal­culation of nonreactive scattering are classified. The classification is based on the essential characteristics of methods, not their detailed technical aspects. As a result the potential efficiency of each class of methods can be determined. Methods derived from differential formalism (time-independent and time-dependent Schroe­dinger equations) and from integral formalism (Lippmann­-Schwinger equation) are reviewed. The most efficient class of differential methods are found to be time­ independent perturbation propagation channel methods. Integral and differential methods are found to be very similar. There seems to be no room for any further dra­matic improvements in exact nonreactive quantum methods.

Part 2. Most calculations of the vibrational scattering of diatom-atom collisions use the breathing sphere approximation (BSA) of orientation-averaging the intermolecular potential. The resulting angularly sym­metric potential cannot cause rotational scattering. We determine the error introduced by the BSA into observables of the vibrational scattering of low-energy homonuclear diatom-atom collisions by comparing two quantum mechanical calculations, one with the BSA and the other with the full angularly asymmetric intermolecular potential. For rea­sons of economy the rotational scattering of the second calculation is restricted by the use of special incomplete channel sets in the expansion of the scattering wavefunction. Three representative collision systems are studied: H₂-A, O₂-He, I₂-He. From our calculations we reach two ­ conclusions. First, the BSA can be used to analyze accurately experimental measurements of vibrational scattering. Sec­ond, measurements most sensitive to the symmetric part of the intermolecular potential are, in order, elastic cross sections, inelastic cross sections and inelastic differen­tial cross sections. Elastic differential cross sections are sensitive to the potential only if the collision is "sticky", with scattering over a wide range of angles; I₂-He is such a collision. Otherwise the potential sensitivity of elastic differential cross sections is con­centrated in the experimentally difficult region of very small angle scattering.

Part 3. The vibrational deexcitation probability, P₁₀, is calculated quantum mechanically over a large ener­gy range for models of three collision systems: O₂-O₂, Cl₂-Cl₂, and Br₂-Br₂. The vibrational deexcitation cross section, σ₁₀, is similarly calculated for the Cl₂-Cl₂ model. P₁₀ and σ₁₀ are obtained for the Lennard-Jones intermolecular potential and three otl1er "well-less" potentials designed to duplicate the scattering of the Lennard-Jones potential. The results emphasize the adiabatic na­ture of potentials with wells and indicate that the acceler­ation approximation for the effect of the well is not valid. The curves of P₁₀ and σ₁₀ as a function of initial translational energy are used to obtain exact collision numbers. These numbers are compared to the results of SSH theory. SSH theory is found to predict collision numbers with reasonable accuracy except at low temperatures. SSH theory is also not suitable for analyzing experimental collision numbers for the well depth potential parameter.

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