  We consider a generalisation of the p+ip pairing Hamiltonian with external
interaction terms. These terms allow for the exchange of particles between the
system and its environment. As a result the u(1) symmetry associated with
conservation of particle number, present in the p+ip Hamiltonian, is broken.
Nonetheless the generalised model is integrable. We establish integrability
using the Boundary Quantum Inverse Scattering Method, with one of the
reflection matrices chosen to be non-diagonal. We also derive the corresponding
Bethe Ansatz Equations, the roots of which parametrise the exact solution for
the energy spectrum.
