Failure of bulk-correlation-length scaling for the superfluid density of confinedHe4

We present new measurements of the superfluid density of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ confined between sheets of Mylar at 4600 Å average separation. These data show a full range of behavior, from bulk, to finite size, to two dimensional. We analyze these data, as well as those from three other experiments, to test predictions of finite-size scaling theory. We use a scaling function from the Ginzburg-Pitaevskii-Mamaladze theory, as well as a function we suggest in analogy to the work of Josephson. We find that only this latter function is consistent with the data. Furthermore, we find that the deviations from bulk behavior do not scale with the bulk-correlation-length exponent. We find this to be in quantitative agreement with earlier results for the specific heat of confined helium.