  The quantum phases of superconductivity and superfluidity are characterised
mathematically by the Yang concept of Off-Diagonal Long Range Order (ODLRO),
related to the existence of a large eigenvalue of the density matrix. We
analyse how the Yang criterion applies for various Hamiltonians commonly
employed to describe superfluid-type correlations in atomic nuclei. For
like-particle pairing Hamiltonians the behaviour of the largest eigenvalue of
two-body density matrix shows a clear evidence for a transition between a
normal to a paired phase. However, this is not the case for the isoscalar
proton-neutron pairing interactions acting in self-conjugate nuclei.
