A microscopic calculation of the effective mass of one ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ impurity in homogeneous liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ at zero temperature is performed for an extended Jastrow-Slater wave function, including two- and three-body dynamical correlations and also backflow correlations between the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ atom and the particles in the medium. The effective mass at equilibrium density, m〈main${\mathrm{〉}}_4^{\mathrm{*}}$/${\mathit{m}}_4$=1.21, is in very good agreement with the recent experimental determination by Edwards et al. The three-particle correlations appear to give a small contribution to the effective mass and different approximations for the three-particle distribution function give almost identical results for ${\mathit{m}}_4^{\mathrm{*}}$/${\mathit{m}}_4$.

The role played by the correlations depending on the third component of spin, ${\mathrm{\sigma }}_{\mathit{z}}$-dependent correlations, in the description of the ground state of liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is studied. With this aim, the competition among this kind of correlations and central three-body and blackflow correlations has been analyzed. This has been done using a generalization of Fermi hypernetted chain equations. Special attention has been paid to the approximation of the elementary diagrams using the two most efficient approximations: the scaling and the interpolating equation. The obtained results for the energy with both approximations are similar for all the cases studied. The increment of the energy supplied by ${\mathrm{\sigma }}_{\mathit{z}}$-dependent correlaions is not modified by the inclusion of three-body correlations. However, this increment disappears when blackflow correlations are introduced because of a strong competition between both mechanisms of correlation.

We study the ground state properties of doubly closed shell nuclei ${}^{16}\mathrm{O}$ and ${}^{40}\mathrm{Ca}$ in the framework of correlated basis function theory using state dependent correlations, with central and tensor components. The realistic Argonne $v_{14}$ and $v_8^{\prime }$ two-nucleon potentials and three-nucleon potentials of the Urbana class have been adopted. By means of the Fermi hypernetted chain integral equations, in conjunction with the single operator chain approximation, we evaluate the ground state energy, one- and two-body densities and electromagnetic and spin static responses for both nuclei. In ${}^{16}\mathrm{O}$ we compare our results with the available Monte Carlo and coupled cluster ones and find a satisfying agreement. As in the nuclear matter case with similar interactions and wave functions, the nuclei result underbound by 2–3 MeV/nucleon.

The perturbative-variational method is used with a nonorthogonal basis set whose elements are combinations of two harmonic-oscillator functions symmetrically shifted around the origin in order to approximate the eigenvalues and eigenfunctions of the two-well anharmonic-oscillator potential [V(x)=-${\mathit{Z}}^2$ ${\mathit{x}}^2$+${\mathit{x}}^4$ with ${\mathit{Z}}^2$>0]. This basis set is rather adequate for this potential and allows one to calculate not only the ground-state energy but also the energy of the excited states with very high precision.