  The form of the wave function at three-electron coalescence points is
examined for several spin states using an alternative method to the usual Fock
expansion. We find that, in two- and three-dimensional systems, the
non-analytical nature of the wave function is characterized by the appearance
of logarithmic terms, reminiscent of those that appear as both electrons
approach the nucleus of the helium atom. The explicit form of these
singularities is given in terms of the interelectronic distances for a doublet
and two quartet states of three electrons in a harmonic well.
