Self-consistent calculation of the thermodynamic potential for superfluid states inHe3nearTc

A self-consistent diagram technique is developed in terms of a 4 × 4 Green's function and a symmetrized 4 × 4 × 4 × 4 interaction vertex to investigate the effect of spin fluctuations on the self-energy and thermodynamic potential in superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. In addition to reproducing the results of Brinkman, Serene, and Anderson (BSA), the resulting $\tilde{T}$-matrix approximation leads to the appearance of a new class of anomalous diagrams not considered by BSA. These new contributions involve a coupling of the particle-particle and particle-hole channels and give rise to an effective paramagnetic enhancement of the particle-particle $T$ matrix below $T_c$. They are shown to further increase the stability of the Anderson-Morel state relative to that of the Balian-Werthamer state near $T_c$. Results are stated in terms of the five fourth-order invariants. The specific-heat discontinuity is calculated and discussed in the context of recent experimental results.