Electrostatic Analogy for Integrable Pairing Force Hamiltonians

Abstract For the exactly solved reduced BCS model an electrostatic analogy exists; in particular it served to obtain the exact thermodynamic limit of the model from the Richardson Bethe ansatz equations. We present an electrostatic analogy for a wider class of integrable Hamiltonians with pairing force interactions. We apply it to obtain the exact thermodynamic limit of this class of models. To verify the analytical results, we compare them with numerical solutions of the Bethe ansatz equations for finite systems at half-filling for the ground state.