Solutions of nuclear pairing

We give the exact solution of orbit dependent nuclear pairing problem between two nondegenerate energy levels using the Bethe ansatz technique. Our solution reduces to previously solved cases in the appropriate limits including Richardson's treatment of reduced pairing in terms of rational Gaudin algebra operators.

Figure 1

Energies for two particle pairs with $j_1=3/2$ and $j_2=5/2$. Here $\vartheta$ describes the occupation amplitudes as described in the text and $\Delta ={\varepsilon }_{j_1}-{\varepsilon }_{j_2}$ is the separation between single particle levels.