RECENT PROGRESS IN THE THEORY OF ROTONS IN SUPERFLUID HE-4

The excitation spectrum of superfluid He-4 is discussed on the basis o f a shadow wave function. The potential and kinetic energies of the ex citations are computed at different densities. The theory has been ext ended at finite temperature and we obtain the roton contribution to th e radial distribution function, to the depletion of the condensate and to the dynamical structure factor S(q,omega). We present also the fir st realistic microscopic computation of the roton energy at finite T. Possible role of thermally excited vortices on rotons is considered. W ith a simple model we show that some discrepancies between the linewid th of the roton response in neutron and in Raman scattering can be res olved.