Growth 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>Layers from Surfaces of Nearly Saturated Solutions 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 Superfluid<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>

The problem of the growth of the ${\mathrm{He}}^{3}$ phase from a free surface of a nearly saturated solution of ${\mathrm{He}}^{3}$ in superfluid ${\mathrm{He}}^{4}$ at zero temperature is considered. Using a Fermi-liquid theory modified to account for the finite thickness of the ${\mathrm{He}}^{3}$ phase by introducing a distortion of the Fermi surface, we find that the number of ${\mathrm{He}}^{3}$ layers ${N}_{L}$ in the ${\mathrm{He}}^{3}$ phase increases as the ${\mathrm{He}}^{3}$ chemical potential ${\ensuremath{\mu}}_{3}$ approaches its bulk value ${\ensuremath{\mu}}_{0}^{3}$ as ${N}_{L}\ensuremath{\sim}{({\ensuremath{\mu}}_{3}^{0}\ensuremath{-}{\ensuremath{\mu}}_{3})}^{\ensuremath{-}\frac{1}{2}}$. This prediction is in agreement with recent experimental results of Guo, Edwards, Sarwinski, and Tough.

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