Bounds for the superfluid fraction from exact quantum Monte Carlo local densities

For solid He-4 and solid p-H-2, using the flow-energy-minimizing one-body phase function and exact T=0 K Monte Carlo calculations of the local density rho(r), we have calculated the phase function, the velocity profile, and upper bounds for the superfluid fraction f(s). At the melting pressure for solid He-4, we find that f(s)<= 0.20-0.21, about ten times what is observed. This strongly indicates that the theory for the calculation of these upper bounds needs substantial improvements.