A 1D Bose gas interacting through $\delta ,{\delta }^{\prime }$ and double $\delta$ function potentials is shown to be equivalent to a $\delta$ anyon gas, allowing an exact Bethe ansatz solution. In the noninteracting limit, it describes an ideal gas with generalized exclusion statistics and solves some recent controversies.

• Received 8 December 1998

DOI:https://doi.org/10.1103/PhysRevLett.83.1275