  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.
