Hard-Sphere Approach to the Excitation Spectrum in Liquid Helium II

The excitation spectrum of a Bose system of hard spheres is obtained in a high-density calculation including multiple scattering processes. The hard-sphere interaction is represented by a non-Hermitian pseudopotential constructed in a previous work, and the $T$-matrix method of Brueckner and Sawada is adopted with modifications to take into account the non-Hermitian property of the Hamiltonian. The inclusion of multiple scattering is found essentially to give a screening effect to the two-body interaction in a many-body medium. The screening factor is studied within certain approximations and is shown to play a very important role in determining the shape of the excitation spectrum. The effect of depletion of particles from the zero-momentum state due to particle interaction is also included in a self-consistent way and is found to be very small. The calculated spectrum is then applied to liquid helium and there is a good qualitative agreement with experiments. Especially, a roton-type dip exists in the spectrum.