Kinetic energies of liquid and solid phases of $^4$He

Kinetic energies of a system of $^4$He are investigated at zero temperature. The multi-weight extension to the diffusion Monte Carlo method is used to implement the Feynman-Hellmann theorem in an effective way. This method allows the quantities of interest to be computed with excellent accuracy. In order to study the importance of symmetry in the kinetic energy calculations, we have considered for the solid phase two guiding wave functions: the Nosanov-Jastrow without boson symmetry and the symmetric Nosanov-Jastrow with boson symmetry. In general very good agreement is found with the experimental data at both the liquid and solid phases.