Superfluidity in asymmetric nuclear matter

The onset of superfluidity in isospin-asymmetric nuclear matter is investigated within the BCS theory. A neutron-proton superfluid state in the channel ${}^3{S}_1$-${}^3{D}_1$ comes about from the interplay between thermal excitations and separation $\delta \mu$ of the two Fermi surfaces. The superfluid state disappears above the threshold value of the density-asymmetry parameter $\alpha {=(n}_n-n_p)/n\simeq 0.35$. For large enough shift between the two Fermi surfaces $\delta \mu =$ $\frac{1}{2}$ $\left({\mu }_n-{\mu }_p\right)$ the transition to the normal state becomes a first-order transition and a second gap solution develops. This solution, however, corresponds to a metastable superfluid state which is unstable with respect to the transition to the normal state.