The description of the properties of liquid Helium is a challenge for any
microscopic many-body theory. In this context, we study the ground state and
the excitation spectrum of one 3He impurity in liquid 4He at T=0 with the
aim of illustrating the power of the correlated basis function formalism in
describing heavily correlated systems. The strong interatomic interaction 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 ground
state wave function, whereas a perturbative expansion including up to two
phonon correlated states must be enforced to study the impurity excitation
energies. The theory describes accurately the experimental spectrum along all
the available momentum range. As empirically shown by the experiments, a marked
deviation from the quadratic Landau-Pomeranchuck behavior is found and the
momentum dependent effective mass of the impurity increases of ∼50 at
q∼1.7 A˚−1 with respect to its q=0 value. Although the main emphasis
is given to the Correlated Basis Function theory, we present also comparisons
with other methods, as diffusion Monte Carlo, variational Monte Carlo with
shadow wave functions and time dependent correlations.Comment: 16 pages, 2 figs, world-scientific latex style. Proceedings of Many
Body X, Seattle, 10-15 Sept. 199