Exchange effects on the excitation spectrum of liquid helium

The contribution to the pair-distribution function from two types of quantum graph is investigated. These graphs have the exchange and collective characters, and are important in the elimination of a divergence and also in the evaluation of the effective mass. A microscopic justification of Landau-type approach with elementary excitations is given. The excitation spectrum and the structure factor are evaluated for a soft potential with a Lennard-Jones-type tail. With the potential parameters chosen so as to have the right sound velocity, and with the effective mass $m^{*}=1.71m$, a good agreement with experiments is achieved. The momentum dependence of $m^{*}$ and the appearance of a particlelike mode in addition to a phononlike mode in the excitation spectrum are discussed.