  We discuss the validity of replacing the complicated three-body confinement
operator of the Y string junction type by three kinds of approximation which
are numerically much simpler to handle: a one-body operator with the junction
point at the centre of mass, a two-body operator corresponding to half the
perimeter of the triangle formed by the three particles, and the average of
both. Two different approaches for testing the quality of the approximations
are proposed: a geometrical treatment based on the comparison of the potential
energy strengths for the various inter quark distances, and a dynamical
treatment based on the comparison of the corresponding effective string
tensions using a hyperspherical approach. Both procedures give very similar
results. It is shown how to simulate the genuine string junction operator by
the approximations proposed above. Exact three-body calculations are presented
in order to compare quantitatively the various approximations and to confirm
our analysis.
