Comparison of log-derivative and renormalized Numerov methods in low-energy two-body collisions

Abstract

Abstract The log-derivative (LOGD) and renormalized Numerov (RN) methods are popularly used in inelastic and reactive scattering calculations. The computational precision of two methods and their improved versions are compared in two-body diatomic and bimolecular collisions at low temperatures. In diatomic 40K-133Cs collision example the single-channel calculations show the solution-improved RN method has the advantage over others when large fixed propagating interval used. The relative error of local scattering length in different propagating sectors are explored. In multi-channel 40K-133Cs collisions the predicted positions of Feshbach resonances by using mapping grid points indicate strong potential-following character in LOGD methods, which is consistent with the analysis on local scattering length in single-channel calculations. In multiple open-channel calculations the elastic and inelastic scatterings and their dependence on collision energy are compared as well. In bimolecular 23Na87Rb-23Na87Rb long-range reactive scattering example the elastic and reactive rate coefficients are investigated. The original LOGD method displays surprisingly relatively high accuracy with less mapping grid points and a wide range of mapping parameters. By increasing the number of mapping grid points the improved LOGD exhibits definitely superiority on precision with proper mapping parameters. We demonstrate our consequent is applicable in other colliding systems.