EXCITATIONS IN SUPERFLUID HE-4 AND THE CONDENSATE

Starting from an accurate representation of the wave function of the g round state and of the phonon-roton excitations based upon the shadow function we present a microscopic density matrix for superfluid He-4. The roton and maxon energy is computed both at zero and at finite temp erature at different densities. The separate contributions of kinetic and potential energy of the roton excitation are computed and we find that a roton lowers the potential energy. The roton contribution to th e depletion of the Bose-Einstein condensate n0 is computed. Excitation of 5 to 10 rotons is needed for the depletion of one atom from the co ndensate and no simple relation is found between the T dependence of n 0 and of g(r). Other quantities we compute as function of T are the st atic structure factor and the strength of the 'one-phonon' peak of the dynamical structure factor. Comparison of our results with experiment gives some evidence that additional excitations become important abov e about 2K.