Application of finite element methods for inelastic and reactive scatterings

Abstract

Redial wavefunctios in quantum scattering calculations are expanded in terms of two shape functions for each finite element. This approach is the R matrix version of Kohn``s variational method and also directly applicable to S matrix in the log-derivative version. The linear algebra involved amounts to solving definite banded systems. In this basis set method, R matrix or log-derivative matrix is greatly simplified and the computational effort is linearly proportional to the number of radial basis functions, promising computational efficiencies for large scale calculations. Convergences for test cases are also reasonably rapid. Coupled channel equations for collinear quantum reactive scattering process in hyperspherical polar coordinate are described in a discrete variable representation. In hyperspherical olar coordinate all channel orbitals are incorporated under one hyperradius and hence all computaional advantages of using finite element basis in inelastic scattering porcesses remains valid in reactive scattering cases. The corresponding pointwise representation of variational R matrix is presented. The potential is diagonal in discrete variable representations, which gives great computational savings. In interaction region, the point basis set has good convergence and the radial wavefunction is not highly oscillatory. The variational R matrix can be calculated with moderate size of both the point basis set and the finite element basis for the radial wavefunction.