Numerical Evaluation of Cuspoid and Bessoid Oscillating Integrals for Applications in Chemical Physics

TL;DR

This paper presents a new adaptive contour algorithm for the accurate numerical evaluation of cuspoid and bessoid oscillating integrals, which are important in chemical physics phenomena like atomic collisions and spectroscopy.

Contribution

The paper introduces a novel adaptive contour algorithm for computing oscillatory integrals, improving accuracy and stability in chemical physics applications.

Findings

Successfully evaluated cuspoid and bessoid integrals numerically

Demonstrated the algorithm's effectiveness on swallowtail and bessoid integrals

Enhanced computational stability for oscillatory integrals

Abstract

Oscillating integrals often arise in the theoretical description of phenomena in chemical physics, in particular in atomic and molecular collisions, and in spectroscopy. A computer code for the numerical evaluation of the oscillatory cuspoid canonical integrals and their first-order partial derivatives is described. The code uses a novel adaptive contour algorithm, which chooses a contour in the complex plane that avoids the violent oscillatory and exponential natures of the integrand and modifies its choice as necessary. Applications are made to the swallowtail canonical integral and to a bessoid integral.