Spin-fluctuation theory of strong coupling corrections to the free energy in superfluid 3He

Abstract

Previous spin-fluctuation theories yielding the strong coupling corrections ..delta..beta-bar/sub i/ to the five coefficients of the fourth-order invariants in the free energy functional are extended. First, the superfluid part of the susceptibility is calculated up to order ..delta../sup 4/for all momenta and frequencies and the contribution arising from p-wave fluctuations of the order parameter is included. Then the frequency sums yielding the ..delta..beta-bar/sub i/ are calculated by taking into account the full momentum and frequency dependence of the superfluid susceptibility and the spin fluctuation propagator. The results for the ..delta..beta-bar/sub i/ are plotted vs. a cutoff q/sub c/ on the momentum integration for spin-fluctuation parameters IequivalentN(0)I=0.75 and I=0.95. The cutoff takes into account in a rough way the effect of additional terms in the free energy functional which were neglected in previous theories. These additional terms are due to the implicit dependence of the superfluid susceptibility on the spin-fluctuation parameter I via the gap parameter ..delta... The gap equation providing the relation between ..delta.. and I is derived in the weak coupling approximation. The cutoffs obtained by fitting the experimental values of the three combinations of ..delta..beta-bar/sub i/(arising from the measured specific heat discontinuities on the melting curve) are comparablemore » to the cutoff obtained from the spin-fluctuation contribution to the weak coupling free energy (q/sub c/=0.3(2k/sub F/) for I=0.75). The corrections due to the momentum and frequency dependence of the superfluid susceptibility and the spinfluctuation propagator are large and point in the direction of better agreement with experiment: The ratio R/sub 1/ =..delta..beta-bar/sub 5//(..delta..beta-bar/sub 2/+..delta..beta-bar/sub 4/) decreases from 2 to about 1.2. It is concluded that spin-fluctuation theory in its present form cannot account quantitatively for the measured specific heat discontinuities on the melting curve.« less