Conventional BCS, Unconventional BCS, and Non-BCS Hidden Dineutron Phases in Neutron Matter

The nature of pairing correlations in neutron matter is re-examined. Working within the conventional approximation in which the $nn$ pairing interaction is provided by a realistic bare $nn$ potential fitted to scattering data, it is demonstrated that the standard BCS theory fails in regions of neutron number density where the pairing constant $\lambda$, depending crucially on density, has a non-BCS negative sign. We are led to propose a non-BCS scenario for pairing phenomena in neutron matter that involves the formation of a hidden dineutron state. In low-density neutron matter where the pairing constant has the standard BCS sign, two phases organized by pairing correlations are possible and compete energetically: a conventional BCS phase and a dineutron phase. In dense neutron matter, where $\lambda$ changes sign, only the dineutron phase survives and exists until the critical density for termination of pairing correlations is reached at approximately twice the neutron density in heavy atomic nuclei.