  Universal behaviour in few-bosons systems close to the unitary limit, where
two bosons become unbound, has been intensively investigated in recent years
both experimentally and theoretically. In this particular region, called the
unitary window, details of the inter-particle interactions are not important
and observables, such as binding energies, can be characterized by a few
parameters. With an increasing number of particles the short-range repulsion,
present in all atomic, molecular or nuclear interactions, gradually induces
deviations from the universal behaviour. In the present letter we discuss for
the first time a simple way of incorporating non-universal behaviour through
one specific parameter which controls the smooth transition of the system from
universal to non-universal regime. Using a system of $N$ helium atoms as an
example we calculate their ground state energies as trajectories within the
unitary window and also show that the control parameters can be used to
determine the energy per particle in homogeneous systems when $N \rightarrow
\infty$.
