Low-Temperature Density and Solubility of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>in Liquid<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>under Pressure

The molar volumes of liquid mixtures of ${\mathrm{He}}^{3}$ in ${\mathrm{He}}^{4}$ up to 10 molar% have been measured to 22 atm pressure and to 50 mK using a dielectric technique. The single-phase measurements provide a determination of the Bardeen-Baym-Pines (BBP) parameter $\ensuremath{\alpha}$ under pressure. A weaker pressure dependence is found than in the measurements of Boghosian and Meyer. The ground-state kinetic energy for pure ${\mathrm{He}}^{4}$ is deduced from $\ensuremath{\alpha}$. The two-phase measurements indicate that the solubility at 50 mK of ${\mathrm{He}}^{3}$ in ${\mathrm{He}}^{4}$ rises from (6.6 \ifmmode\pm\else\textpm\fi{} 0.1)% at $P=0$ to a maximum of (9.5 \ifmmode\pm\else\textpm\fi{} 0.12)% at 10 atm; it then drops to (8.3 \ifmmode\pm\else\textpm\fi{} 0.14)% at 22.5 atm. This behavior is found to be consistent with the BBP effective interaction theory using the Ebner potential.

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