Strong coupling corrections to the Ginzburg-Landau theory of superfluid ³He

In the Ginzburg-Landau theory of superfluid ³He, the free energy is expressed as an expansion of invariants of a complex order parameter. Strong coupling effects, which increase with increasing pressure, are embodied in the set of coefficients of these order-parameter invariants [ A. J. Leggett Rev. Mod. Phys. 47 331 (1975); E. V. Thuneberg Phys. Rev. B 36 3583 (1987); J. Low Temp. Phys. 122 657 (2001)]. Experiments can be used to determine four independent combinations of the coefficients of the five fourth-order invariants. This leaves the phenomenological description of the thermodynamics near T_c incomplete. Theoretical understanding of these coefficients is also quite limited. We analyze our measurements of the magnetic susceptibility and the NMR frequency shift in the B phase which refine the four experimental inputs to the phenomenological theory. We propose a model based on existing experiments, combined with calculations by Sauls and Serene Phys. Rev. B 24 183 (1981) of the pressure dependence of these coefficients, in order to determine all five fourth-order terms. This model leads us to a better understanding of the thermodynamics of superfluid ³He in its various states. We discuss the surface tension of bulk superfluid ³He and predictions for novel states of the superfluid such as those that are stabilized by elastic scattering of quasiparticles from a highly porous silica aerogel.