We study the weak-tunnelling limit for a system of cold 40K atoms trapped in
a one-dimensional optical lattice close to an s-wave Feshbach resonance. We
calculate the local spectrum for three atoms at one site of the lattice within
a two-channel model. Our results indicate that, for this one-dimensional
system, one- and two-channel models will differ close to the Feshbach
resonance, although the two theories would converge in the limit of strong
Feshbach coupling. We also find level crossings in the low-energy spectrum of a
single well with three atoms that may lead to quantum phase transition for an
optical lattice of many wells. We discuss the stability of the system to a
phase with non-uniform density.Comment: 10 pages, 5 figure
