HELMHOLTZ-RESONATOR MEASUREMENTS OF THE SUPERFLUID DENSITY OF LIQUID-HE-4 IN SUBMICROMETER-DIAMETER CHANNELS

The dependence of the effective relative superfluid density ρspρ upon temperature T has been measured in 0.10, 0.08, 0.05, and 0.03-μm-diameter cylindrical pores in 5.0-μm-thick polycarbonate films (Nuclepore) using a superfluid Helmholtz resonator. We observe that ρspρ lies below the bulk relative superfluid density ρsbρ, and that near Tλ, ρspρ for a given pore size is represented well by the relationship ρspρ=C(t-t01)ζ, where t(Tλ-T)Tλ, C2.46±0.07, ζ=0.675±0.020, and t01 is an effective pore-size-dependent reduced onset temperature equal to (0.26, 0.60, 0.89, and 2.84) × 10-3 for the four pore sizes, respectively. At the same time we find that over a broad range of temperature, including the region near Tλ, ρspρ for a given pore size can be represented well by the relationship ρspρ=D[ρsb(t)ρ-ρsb(t02)ρ], where D is a constant and t02 is an alternative effective reduced onset temperature. However, this form, which is linear in ρsbρ, has an asymptotic behavior different from that above as ρspρ→0 and yields for each pore size a value for t02 which is more than a factor 2 smaller than the value for t01 above. © 1979 The American Physical Society.