  Within the hyperspherical framework, the solution of the time-independent
Schroedinger equation for a n-particle system is divided into two steps, the
solution of a Schroedinger like equation in the hyperangular degrees of freedom
and the solution of a set of coupled Schroedinger like hyperradial equations.
The solutions to the former provide effective potentials and coupling matrix
elements that enter into the latter set of equations. This paper develops a
theoretical framework to determine the effective potentials, as well as the
associated coupling matrix elements, for few-body systems with finite angular
momentum L=1 and negative and positive parity. The hyperangular channel
functions are expanded in terms of explicitly correlated Gaussian basis
functions and relatively compact expressions for the matrix elements are
derived. The developed formalism is applicable to any n; however, for n greater
or equal to 6, the computational demands are likely beyond present-day
computational capabilities. A number of calculations relevant to cold atom
physics are presented, demonstrating that the developed approach provides a
computationally efficient means to solving four-body bound and scattering
problems with finite angular momentum on powerful desktop computers. Details
regarding the implementation are discussed.
