Thermal expansion coefficient near the superfluid transition ofHe4in an aerogel

We measured the isobaric thermal expansion coefficient ${\mathrm{\beta }}_{\mathit{P}}$ near the superfluid transition of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ in an aerogel along six isobars between 3 and 24 bars. The data yield the specific-heat exponents α and α’ and amplitude ratio A/A’. Fits by power laws in t≡T/${\mathit{T}}_{\mathit{c}}$-1, where ${\mathit{T}}_{\mathit{c}}$ is the transition temperature, produced α≃-0.6 and α’≃-1.0≠α. Including an analytic background a×t permitted α=α’≃-0.59, but required a very large coefficient a and yielded A’/A≃0. The exponents are inconsistent with that of ${\mathrm{\rho }}_{\mathit{s}}$ and hyperscaling in three dimensions.