  We present detailed calculations of bound and scattering states of dimers and
trimers of He to produce highly accurate data and to test a non-relativistic
three-body code currently in development for public distribution. For these
systems, uncertainties and inaccuracies in the fundamental constants frequently
used in published works can substantially exceed numerical errors. Our
benchmark calculations include specific estimates of the numerical accuracy of
the calculations, and also explore sensitivity to fundamental constants and
their uncertainties. The use of an inexact coupling constant in the previous
calculations leads to 0.08% error for the ground state energy, 0.3% error for
the excited state energy and up to 0.15% error for the atom-dimer scattering
length in the system of three $^4$He atoms. The corresponding errors for the
unsymmetric $^{4}$He$_{2}^{3}$He system are 0.3% for the bound state energy and
0.03% for the atom-dimer scattering length.
