Approximate Differential Cross Sections at Large Scattering Angles for Simple Repulsive Potentials

Semiclassical transition probabilities by an asymptotic evaluation of the S matrix for elastic and inelastic collisions. Bessel uniform approximationThe uniform approximation to the differential elastic scattering cross section is extended to allow direct comparison of approximated cross sections with cross sections computed by exact evaluation of the partial wave sum using WKB phase shifts. Results of calculations are presented and an assessment is made of the accuracy and utility of the uniform approximation.

Section: Calculation Of Cross Sectionsmentioning

confidence: 99%

On an evaluation of the accuracy of the uniform semiclassical approximation for differential elastic scattering cross sections

Mullen

Thomas

1973

Large Angle Elastic Scattering of Ar+ by He

Chiang

Gislason

Mahan

et al. 1971

Self Cite

Measurement of accurate differential cross sections for systems of the type ``heavy projectile light target'' are shown to be practical, provided measurements are restricted to large center-of-mass scattering angles θ. As an example, cross sections for the system Ar+−He have been measured from θ=60–180° in the energy range 2.7–9.1 eV. Using two-parameter repulsive potentials the results are inverted to yield a potential which reproduces the scattering at all energies. Dramatic evidence is given that potentials of the form V(r)=K/r3 are unsatisfactory for fitting the intermolecular potential in the region of 1–10 eV. The potential derived from these experiments is an average of two molecular potentials, since both the X 2Σand A 2Π states of Ar+−He correlate to ground state atoms. Comparisons are made with theoretical estimates of the two molecular potentials and with the Ar−He+ and Ar−He potentials.

Exact Series Solution of Classical Deflection Angle for Repulsive Inverse Power Potential

Gislason

1972