  We study cold atomic gases with a contact interaction and confined into
one-dimension. Crossing the confinement induced resonance the correlation
between the bosons increases, and introduces an effective range for the
interaction potential. Using the mapping onto the sine-Gordon model and a
Hubbard model in the strongly interacting regime allows us to derive the phase
diagram in the presence of an optical lattice. We demonstrate the appearance of
a phase transition from a Luttinger liquid with algebraic correlations into a
crystalline phase with a particle on every second lattice site.
