  A contact potential describing an effective interaction between atomic $^4$He
reproducing the results obtained with the HFDHE2 potential by Aziz et al. is
employed to study the resulting equation of state by means of Quantum Monte
Carlo calculations. \cblack The energy per particle and the pair distribution
functions were investigated as a function of the ultraviolet cutoff $\Lambda$.
The results suggest that not only the mean field properties of the system, such
as the energy and the saturation density, are correctly reproduced, but also
very microscopic quantities such as the pair distribution function are seen to
converge towards the exact results when extrapolating for
$\Lambda\rightarrow\infty$.
