A microscopic look at liquid helium: The He-3 impurity case

The description of the properties of liquid Helium is a challenge for any m icroscopic many-body theory. In this context, we study the ground state and the excitation spectrum of one He-3 impurity in liquid He-4 at T = 0 with the aim of illustrating the power of the correlated basis function formalis m in describing heavily correlated systems. The strong interatomic interact ion and the large density require the theory to be pushed to a high degree of sophistication. A many-body correlation operator containing explicit two - and thre-particle correlation functions is needed to obtain a realistic g round state wave function, whereas a perturbative expansion including up to two phonon correlated states must be enforced to study the impurity excita tion energies. The theory describes accurately the experimental spectrum al ong all the available momentum range. As empirically shown by the experimen ts, a marked deviation from the quadratic Landau-Pomeranchuck behavior is f ound and the momentum dependent effective mass of the impurity increases of similar to 50 % at q similar to 1.7 Angstrom (-1) with respect to its q = 0 value. Although the main emphasis is given to the correlated basis functi on theory, we present also comparisons with other methods, as diffusion Mon te Carlo, variational Monte Carlo with shadow wave functions and time depen dent correlations.