SUPERFLUID TRANSITION OF HE-4 IN ULTRALIGHT AEROGEL

We present superfluid density and heat capacity results of He-4 entrai ned in 5%, 2%, and 0.5% dense silica aerogel. The superfluid density e xponent shows a systematic decrease towards the bulk He-4 value with d ecreasing aerogel density. Singular contribution to heat capacity is o bserved on both sides of the transition in aerogel of 2% and 0.5% sili ca. In the lightest sample, the scaling law alpha = alpha(1) and the h yperscaling relation 2 - alpha = d nu, = d zeta are satisfied. [S0031- 9007(97)05256-3].