Hyperspherical surface functions for nonzero total angular momentum. I. Eckart singularities

A new hybrid numerical technique which utilizes both the DVR (Discrete Vari able Representation) and FBR (Finite Basis Representation) to solve for the full 5D surface functions in the three-atom problem in hyperspherical coor dinates for nonzero total angular momentum (J not equal 0) is reported. Thi s method accurately treats the Eckart singularities in the kinetic energy o perator which occur at both the north pole and equator of the 2D hyperspher e in body-frame coordinates. The effects of the Eckart singularities on the surface function energies for HD2 are investigated and it is shown that an accurate treatment of these singularities is crucial in order to obtain th e correct results. An improper treatment of the Eckart singularities could be a source for some of the discrepancies between recent experimental resul ts and theory for the reaction H+D-2-->HD+D. (C) 1999 American Institute of Physics. [S0021-9606(99)00914-9].