DISTRIBUTED APPROXIMATING FUNCTION-THEORY FOR AN ARBITRARY NUMBER OF PARTICLES IN A COORDINATE SYSTEM-INDEPENDENT FORMALISM

A general, multidimensional distributed approximating function theory is developed that applies to any system which has one possible configurational representation in Cartesian variables. That is, the configuration of the system can be expressed as a generalized N-dimensional vector which has the usual transformation properties under multidimensional rotations. In particular, the theory is applicable to a scattering system with an arbitrary number, A, of scattering centers and projectiles (atoms), for which N = 3A. The approach makes possible the realization of distributed approximating functions (DAFs) in any orthogonal, curvilinear coordinates including spherical polar, cylindrical polar, and hyperspherical, as well as elliptic and parabolic coordinates.