Novel Semi-Classical Cross Section Solver of Particle-Particle and Particle-Cluster Interactions for the inclusion of Heavy Ion Impacts and Cluster Formation in Plasma Simulations

A main problem in cluster formation models is the lack of fundamental data describing particle-particle and particle-cluster interactions, such as interatomic potentials, differential scattering cross-sections and total cross-sections. Calculation of the classical differential scattering cross section with analytical calculations are practical only for the simplest cases, and experiments measuring cross-sections are seldomly performed for large molecules or clusters due to their complexity of interpretation. In this work, a new software tool is presented for the solution of the semi-classical scattering problem, and then verification studies are performed. The code is implemented in Python, with non-dimensionalization, and Chebyshev Polynomial root finding. Chebyshev polynomial root finding is used to calculate roots of the distance of closest approach equation for attractive-repulsive potentials, since Newton solvers frequently fail for potentials with multiple real roots. This allows the solving of a wide variety of attractive-repulsive potentials. Numerical explorations are run for reactive plasmas containing metals, such as uranium-oxygen and aluminum-oxygen plasmas, which lack theoretical or experimental cross-sections.