S-MATRIX VERSION OF THE HULTHEN-KOHN VARIATIONAL PRINCIPLE FOR QUANTUM REACTIVE SCATTERING USING FINITE-ELEMENTS - CONCEPTS, DISCRETIZATIONS AND INTERNAL BASIS-SETS

The finite element (FE) method can be applied to solve inelastic and r eactive scattering problems for triatomic systems. We use an S-matrix version of the Hulthen-Kohn variational principle for a three-dimensio nal scattering problem. The asymptotic wavefunction is described by an alytical functions and the interaction part by a combination of finite element and discrete variable representation (DVR) functions. Transla tional and vibrational coordinates are described by FEs and for the an gular part a DVR-discretization is used. The FE method is used in orde r to calculate eigenfunctions for the interior region of the potential at each given DVR-angle and from this set of functions the full three -dimensional eigenfunctions are calculated and are used as a new basis for scattering. The grid is chosen such that it covers all reaction c hannels and the calculations are done by using only one set of Jacobi coordinates. Results obtained by choosing different FE-discretizations , raising the number of elements and increasing the number of internal three-dimensional eigenfunctions, are compared.