  We investigate finite-range effects in systems with three identical bosons.
We calculate recombination rates and bound state spectra using two different
finite-range models that have been used recently to describe the physics of
cold atomic gases near Feshbach resonances where the scattering length is
large. The models are built on contact potentials which take into account
finite range effects; one is a two-channel model and the other is an effective
range expansion model implemented through the boundary condition on the
three-body wave function when two of the particles are at the same point in
space. We compare the results with the results of the ubiquitous
single-parameter zero-range model where only the scattering length is taken
into account. Both finite range models predict variations of the well-known
geometric scaling factor 22.7 that arises in Efimov physics. The threshold
value at negative scattering length for creation of a bound trimer moves to
higher or lower values depending on the sign of the effective range compared to
the location of the threshold for the single-parameter zero-range model. Large
effective ranges, corresponding to narrow resonances, are needed for the
reduction to have any noticeable effect.
