  Ultracold atoms placed in a tight cigar-shaped trap are usually described in
terms of the Lieb-Liniger model. We study the extensions of this model which
arise when van der Waals interaction between atoms is taken into account. We
find that the corrections induced by the finite range of interactions can
become especially important in the vicinity of narrow Feshbach resonances and
suggest realistic schemes of their experimental detection. The interplay of
confinement and interactions can lead to effective transparency where the
one-dimensional interactions are weak in a wide range of parameters.
