Using fourth-sound techniques, we have measured the depression of the superfluid fraction of 3 He confined in small pores of packed powder over wide temperature (0.2 < T/T c <1) and pressure (0.5 < p < 20 bars) ranges. From the analysis of the data we determine the magnitude and the pressure dependence of the healing length. The healing length decreases from 520 A at 0.5 bar to 200 A at 20 bars. The values are in fair agreement with those expected from the BCS expression.PACS numbers: 67.50.Fi, 74.50.-l-r When a superfluid is confined in a sufficiently restricted geometry, the macroscopic order parameter describing the superfluid state becomes distorted by the presence of the boundary wall. 1 " 3 The nature of distortion will be determined by the particular boundary conditions that the wall imposes on the order-parameter function. Theoretical and experimental studies aimed at probing the boundary conditions for superfluid 3 He are currently under active research. 4 Understanding that the boundary conditions will be important in the design of an appropriate weak link for observing the long-sought analog of the Josephson effect in superfluid 3 He. 5 ' 6 Interpretation of experiments on superfluid-3 He films will be related to the boundary conditions. An important parameter in these phenomena is the healing length which determines the characteristic distance over which the order parameter decreases from its bulk value to zero near a wall. In this paper we describe a systematic determination of the healing length over a wide pressure range from the analysis of the measured superfluid fraction of 3 He confined in the pores of packed powder.Ambegaokar, de Gennes, and Rainer 1 showed that the nature of scattering of quasiparticles at a solid wall plays a crucial role in the determination of the boundary conditions. If the scattering is completely diffusive, they showed that the perpendicular (to the wall surface) component of the order parameter vanishes at the wall and that the parallel component is depressed from the bulk value by a factor of ~£O/£(JT). Here £n is the zerotemperature coherence length and %(T) is the temperature-dependent healing length. Recently, Buchholtz 7 showed that if the surface is bumpy at random on the scale of inverse Fermi wave number (~5 A) the parallel component also vanishes at the surface. It seems reasonable to assume that the powder used in our experiment presents diffuse scattering surfaces and that all components of the order parameter vanish at the surface.The Ginsburg-Landau (GL) equations, including the gradient terms for superfluid 3 He, have been derived by Ambegaokar, de Gennes, and Rainer. ] The GL equations define a natural length scale given by the healing length for the spatial variation of the order parameter. Minimizing the GL free-energy functional by variational calculation, Ebisawa and Arai 8 have shown that if a cylindrical pore of radius R is filled with superfluid 3 He-Z? whose order parameter obeys the above boundary conditions, the average superfluid density in th...
