Asymptotic Bethe ansatz for the Sutherland–Römer model with open boundary conditions Original Research Article

By constructing the reflection spin-Dunkl operators, the integrable Sutherland–Römer model (SRM) with open boundary condition is established, which describes a one-dimensional, two-component, quantum many-particle system in which like particles interact with a pair potential g(g+1)/sinh2(r), while unlike particles interact with a pair potential −g(g+1)/cosh2(r). By solving the Schrödinger equation and using the properties of the hypergeometric functions and gamma functions, the two-particle scattering matrix and the reflection matrix are obtained in the framework of the asymptotic Bethe ansatz method. The Bethe ansatz equations of the system are obtained. The Hamiltonians of SRM with some other open boundary conditions are expressed explicitly. Our method can be generalized, as a example, to the boundary Calogero–Sutherland model which is also constructed by the reflection spin-Dunkl operators.