Limits on Bose-Einstein condensation in confined solidH4e

Abstract

We report neutron-scattering measurements of the Bose-Einstein condensate (BEC) fraction, ${n}_{0}$, in solid helium that has a large surface to volume $(S/V)$ ratio. Rittner and Reppy observed large superfluid fractions, ${\ensuremath{\rho}}_{S}/\ensuremath{\rho}$, in large $S/V$ samples with ${\ensuremath{\rho}}_{S}/\ensuremath{\rho}$ approximately proportional to $S/V$, up to ${\ensuremath{\rho}}_{S}/\ensuremath{\rho}=20%$ at $S/V=150\text{ }{\text{cm}}^{\ensuremath{-}1}$. Our goal is to reveal whether there is BEC associated with these large ${\ensuremath{\rho}}_{S}/\ensuremath{\rho}$. Our solid volume is $100\text{ }{\text{cm}}^{3}$ of commercial grade helium at 41 bars pressure $({T}_{c}\ensuremath{\simeq}200\text{ }\text{mK})$ in a cell that has $S/V=40\text{ }{\text{cm}}^{\ensuremath{-}1}$ that cannot be quenched rapidly. We find no evidence for BEC or algebraic off diagonal long-range order with ${n}_{0}=0.0\ifmmode\pm\else\textpm\fi{}0.3%$ at 65 mK.