Sensitivity analysis of mass effects in rotational energy transfer

This paper examines the sensitivity of rotationally inelastic integral state-to-state cross sections to variations in the masses of the collision partners. We investigate the helium-hydrogenic scattering system with its many physical isotopes and excellent ab initio potential. The collision dynamics are approximated by coupled states-exponential distorted wave (CS-EDW) theory and both cross sections and elementary sensitivity coefficients (partial derivatives of the cross sections with respect to the mass parameters) are calculated. In order to be able to properly interpret these results, we first generate conceptually and computationally simpler distorted wave (CS-DW) cross sections and elementary sensitivities. These perturbative results are analyzed using simple collisional concepts and models. In addition, we present functional forms which predict (or scale) the global behavior of DW cross sections through the mass parameter space. As a quantitative aid in linking EDW cross sections with the DW results, a new type of sensitivity coefficient is introduced which measures the sensitivity of a given EDW cross section to the variation of a single DW cross section or combination thereof.