Bounds for the Superfluid Fraction from Exact Quantum Monte Carlo Local Densities

For solid 4He and solid p-H2, using the flow-energy-minimizing one-body phase function and exact T=0 K Monte Carlo calculations of the local density, we have calculated the phase function, the velocity profile and upper bounds for the superfluid fraction f_s. At the melting pressure for solid 4He 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.