Level Structure of Nuclear Matter and LiquidHe3

Using the $K$ matrix as computed in the study of nuclear matter and liquid ${\mathrm{He}}^3$ as the effective interaction at the Fermi surface, the possible superfluidity of these systems has been investigated. A theory of the cooperative phenomenon valid for particle-particle interaction in states of arbitrary angular momentum has been developed following the methods of Bardeen, Cooper, and Schrieffer. It is found for states of relative angular momentum other than $l=0\mathrm{}$ that the particle pairs must be correlated with respect to an arbitrary direction in the medium. As a result the change of structure of the Fermi surface is angularly dependent. An energy gap does not occur other than for $l=0\mathrm{}$, the particle excitation energy vanishing for certain orientations of the momentum. It is also shown that the specific heat shows a discontinuity at the transition temperature, but somewhat different from the case of $l=0\mathrm{}$.