Polarization potentials and elementary excitations in strongly interacting quantum liquids

A theory of the density fluctuation excitations in liquid He-3 and He-4 which is valid for excitations in the collisionless regime is presented. The restoring force responsible for the density oscillations is the averaged self-consistent field of all the particles in the liquid, which is described by a polarization potential. Effects associated with both the quasi-particle effective mass and the multiphonon excitations are taken into account. The theory is phenomenological, and the key parameters of the theory were determined by fitting to neutron scattering experiments at the saturated vapor pressure. A simple model for the scalar polarization potential was used to extend the calculation to higher pressures. Good agreement was obtained for the variation with pressure of the roton and maxon energies.