Quantum Mechanical (Phase Shift) Analysis of Differential Elastic Scattering of Molecular Beams
- 1 September 1960
- journal article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 33 (3), 795-804
- https://doi.org/10.1063/1.1731265
Abstract
For a spherically symmetrical intermolecular potential V(r)=ϵf(r/σ) the quantum calculation of the elastic scattering cross section dσ(Θ)/dΩ in the c.m. system is carried out as follows. For a given relative velocity (or deBroglie wavelength) and an assumed V(r), the radial wave equation is integrated for successive values of the angular momentum quantum number l, yielding the phase shifts ηι. Then dσ(Θ)dΩ is computed in terms of the series of ηι's in the standard way. A general computational program (following that of K. Smith) is outlined for the evaluation of the radial wave function and the phase shifts, utilizing an IBM 704 computer. Calculations are presented for the L‐J (12, 6) potential function. The results may be concisely represented using the framework provided by the semiclassical treatment of Ford and Wheeler, i.e., in terms of a set of reduced phase constants vs reduced angular momenta at various reduced relative kinetic energies K. Tables and graphs are presented from which the phases may be obtained, to a good approximation, for any given ϵ, σ and K. Computation of the differential and total cross sections from the phase shifts is then readily accomplished.The results are compared with the classical and semiclassical treatments. The problem of tunneling and orbiting is discussedKeywords
This publication has 11 references indexed in Scilit:
- Comparison of Exp-6, L.-J.(12,6), and Sutherland Potential Functions Applied to the Calculation of Differential Scattering Cross SectionsThe Journal of Chemical Physics, 1959
- Semiclassical description of scatteringAnnals of Physics, 1959
- Quantum effects near a barrier maximumAnnals of Physics, 1959
- Symmetry Effects in Gas Kinetics II: Ortho- and Para-hydrogenProceedings of the Physical Society, 1958
- Quantum-mechanical calculation of the second virial-coefficient of helium at low temperaturesPhysica, 1939
- The low-temperature properties of gaseous heliumProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1938
- On the Connection Formulas and the Solutions of the Wave EquationPhysical Review B, 1937
- Über die Streuung von Molekularstrahlen in Gasen. IIThe European Physical Journal A, 1934
- Free paths and transport phenomena gases and the quantum theory of collisions. I.—The rigid sphere modelProceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1933
- Über die Streuung von Molekularstrahlen in Gasen. IThe European Physical Journal A, 1933