  Non-relativistic quantum particles bounded to a curve in R^2 by attractive
contact $\delta$-interaction are considered. The interval between the energy of
the transversal bound state and zero is shown to belong to the absolutely
continuous spectrum, with possible embedded eigenvalues. The existence of the
wave operators is proved for the mentioned energy interval using the
Hamiltonians with the interaction supported by the straight lines as the free
ones. Their completeness is not proved. The curve is assumed C^3-smooth,
non-intersecting, unbounded, asymptotically approaching two different
half-lines (non-parallel or parallel but excluding the "U-case"). Physically,
the system can be considered as a model of long nanostructural channel.
