  We present a mathematically rigorous method suitable for solving three-body
bound state and scattering problems when the inter-particle interaction is of a
hard-core nature. The proposed method is a variant of the Boundary Condition
Model and it has been employed to calculate the binding energies for a system
consisting of three ^4He atoms. Two realistic He-He interactions of Aziz and
collaborators, have been used for this purpose. The results obtained compare
favorably with those previously obtained by other methods. We further used the
model to calculate, for the first time, the ultra-low energy scattering phase
shifts. This study revealed that our method is ideally suited for three-body
molecular calculations where the practically hard-core of the inter-atomic
potential gives rise to strong numerical inaccuracies that make calculations
for these molecules cumbersome.
