Determination of diabatic coupling potentials by the inversion of inelastic atom-atom scattering data: Case studies for He⁺+Ne and Li+I

A general iterative inversion algorithm based on first-order functional sensitivity analysis and Tikhonov regularization is extended for the determination of diabatic coupling potentials from inelastic scattering data. For simplicity, the two-state case is presented here, and it is assumed that the (diagonal) diabatic potentials are known. "Noisy" and "noise-free" numerically simulated data, calculated from model potentials for He⁺+Ne and Li+I, are used to illustrate the method. Various coupling potential trial functions are used, ranging from a constant multiple of the model to a step function. For most cases, the important regions of the coupling potential (i.e., those regions which are most sensitive to the inelastic scattering data, including the region of crossing) are recovered to high precision within four to seven iterations. Those cases which show a small range for convergence may indicate a limit of the present algorithm, based solely on first-order functional derivatives, and the need to extend it to include higher-order terms.