Nucleon-nucleon phase shifts and pairing in neutron matter and nuclear matter

We consider ${}^1{S}_0$ pairing in infinite neutron matter and nuclear matter and show that in the lowest order approximation, where the pairing interaction is taken to be the bare nucleon-nucleon interaction in the ${}^1{S}_0$ channel, the pairing interaction and the energy gap can be determined directly from the ${}^1{S}_0$ phase shifts. This is due to the almost separable character of the nucleon-nucleon interaction in this partial wave. These results put an interaction-independent upper limit on the value of the gap, and on the density where ${}^1{S}_0$ superfluidity disappears in neutron matter and nuclear matter.