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 functiona l sensitivity analysis and Tikhonov regularization is extended for the determination of diabatic coupling potentials from inelastic scatteri ng 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. V arious coupling potential trial functions are used, ranging from a con stant multiple of the model to a step function. For most cases, the im portant regions of the coupling potential (i.e., those regions which a re most sensitive to the inelastic scattering data, including the regi on of crossing) are recovered to high precision within four to seven i terations. Those cases which show a small range for convergence may in dicate a limit of the present algorithm, based solely on first-order f unctional derivatives, and the need to extend it to include higher-ord er terms.