Calculation of angular distributions in complex angular momentum theories of elastic scattering

Abstract

An important practical problem in the application of complex angular momentum techniques to atomic and molecular scattering is the evaluation of Legendre's function of the first kind of complex degree. An exact series representation, that can be summed numerically, has been derived using accelerated convergence techniques. The accuracy of various asymptotic representations for the Legendre function is also investigated. The use of these asymptotic formulae is shown to be valid for most applications of complex angular momentum techniques to atomic and molecular scattering. The asymptotic formulae have a physical interpretation involving backward glories and surface waves.