Finite-Geometry Effects and Onset of Superfluidity inHe3-He4Mixtures nearTλ

Abstract

The amplitude and velocity of second sound near $T_{\lambda }$ and the onset temperature $T_o\mathrm{}\left(X\right)\mathrm{}$ for superfluidity have been measured for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixtures in resonators equipped with superleak transducers. The reduced temperature ${\epsilon }_o=1-\frac{T_o\mathrm{}\left(X\right)\mathrm{}}{T_{\lambda }\mathrm{}\left(X\right)\mathrm{}}$ and the quantity $\frac{l{\rho }_s}{T}$ at ${\epsilon }_o$ vary by factors of about 6 for $X=0\mathrm{} \mathrm{to} 0.4$. The exponents ${\lambda }^{\prime }$ for ${\epsilon }_o=(\frac{d}{d^{*-{\lambda }^{\prime }}}$ and ${\nu }^{\prime }$ for the onset length $l=l^{*}{\epsilon }^{-{\nu }^{\prime }}$ are independent of $X$ to within ± 3%. Contrasting with this behavior is a 20% change of the effective exponent $\zeta$ of $\frac{{\rho }_s}{\rho }=k{\epsilon }^{\zeta }$.