  Here we present a four-channel model that incorporates a magnetically tunable
Feshbach resonance in a system of three atoms that interact via pairwise van
der Waals interactions. Our method is designed to model recent experiments
where the tunability of the scattering length has been used to study three-body
Efimov states, which appear in the limit of a diverging two-body scattering
length. Using this model, we calculate three-body adiabatic and effective
potential curves and study how the strength (or width) of the Feshbach
resonance affects the three-body potential that is connected to the Efimov
effect. We find that the position of the repulsive barrier, which has been used
to explain the so-called van der Waals universality in broad resonances, is
slightly shifted as the narrow resonance limit is approached and that this
shift is correlated to the appearance of two avoided crossings in the adiabatic
energy landscape. More importantly, the attractive well is markedly shifted
upward in energy and is extremely shallow for the narrowest resonance. We argue
that this behavior is connected to the breakdown of van der Waals universality
for weak (narrow) resonances.
