Boundary conditions on internal three-body wave functions - art. no. 042502

For a three-body system, a quantum wave function psi(m)(l) with definite 1 and m quantum numbers may be expressed in terms of an internal wave functio n X-k,(l) which is a function of three internal coordinates. This article p rovides necessary and sufficient constraints on X-k(l) to ensure that the e xternal wave function psi(m)(l) is analytic. These constraints effectively amount to boundary conditions on X-k(l) and its derivatives at the boundary of the internal space. Such conditions find similarities in the (planar) t wo-body problem where the wave function (to lowest order) has the form r(\m \) at the origin. We expect the boundary conditions to prove useful for con structing singularity free three-body basis sets for the case of nonvanishi ng angular momentum.