  We present an energy scaling function to predict, in a specific range, the
energy of bosonic trimers with large scattering lengths and finite range
interactions, which is validated by quantum Monte Carlo calculations using
microscopic Hamiltonians with two- and three-body potentials. The proposed
scaling function depends on the scattering length, effective range, and a
reference energy, which we chose as the trimer energy at unitarity. We obtained
the scaling function as a limit cycle from the solution of the renormalized
zero-range model with effective range corrections. We proposed a simple
parametrization of the energy scaling function. Besides the intrinsic interest
in theoretical and experimental investigations, this scaling function allows
one to probe Efimov physics with only the trimer ground states, which may open
opportunities to identify Efimov trimers whenever access to excited states is
limited.
