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Departures of thermodynamic properties of three-dimensional superfluid $^3$Hefrom the predictions of BCS theory are analyzed. Attention is focused ondeviations of the ratios $\Delta(T=0)/T_c$ and $[C_s(T_c)-C_n(T_c)]/C_n(T_c)$from their BCS values, where $\Delta(T=0)$ is the pairing gap at zerotemperature, $T_c$ is the critical temperature, and $C_s$ and $C_n$ are thesuperfluid and normal specific heats. We attribute these deviations to themomentum dependence of the gap function $\Delta(p)$, which becomes wellpronounced when this function has a pair of nodes lying on either side of theFermi surface. We demonstrate that such a situation arises if the P-wavepairing interaction $V(p_1,p_2)$, evaluated at the Fermi surface, has a signopposite to that anticipated in BCS theory. Taking account of the momentumstructure of the gap function, we derive a closed relation between the tworatios that contains no adjustable parameters and agrees with the experimentaldata. Some important features of the effective pairing interaction are inferredfrom the analysis.Comment: 17 pages, 4 figure

Nodes of the Gap Function and Anomalies in Thermodynamic Properties of the B-Phase of Superfluid 3He