Static response function for longitudinal and transverse excitations in superfluid helium.

The sum rule formalism is used to evaluate rigorous bounds for the density and current static response functions in superfluid He at zero temperature. Both lower and upper bounds are considered. The bounds are expressed in terms of ground state properties (density and current correlation functions) and of the interatomic potential. The results for the density static response significantly improve the Feynman approximation and turn out to be close to the experimental (neutron scattering) data. A quantitative prediction for the transverse current response is given. The role of one-phonon and multi-particle excitations in the longitudinal and transverse channels is discussed. PACS numbers: 67.40.-w, 67.40.Db