BOUNDS FOR THE PHONON-ROTON DISPERSION IN SUPERFLUID HE-4

The sum-rule approach is used to derive upper bounds for the dispersion law omega(o)(q) of the elementary excitations of a Bose superfluid. Bounds are explicitly calculated for the phonon-roton dispersion in superfluid He-4, both at equilibrium (rho = 0.02186 Angstrom(-3)) and close to freezing (rho = 0.026 22 Angstrom(-3)). The bound omega(o)(q) less than or equal to 2S(q) \ chi(q) \(-1), where S(q) and chi(q) are the static structure factor and density response, respectively, is calculated microscopically for several values of the wave vector q. The results provide a significant improvement with respect to the Feynman approximation omega(F)(q) = q(2)[2mS(q)](-1). A further, stronger bound, requiring the additional knowledge of the current correlation function is also investigated. Results for the current correlation function are presented.