We present a density functional for the description of liquid 3He properties at zero temperature in a mean field approximation. Its basic ingredients are a zero-range, particle-and spin-density dependent effective interaction of Skyrme type, and a long-range effective interaction of Lennard-Jones type supplemented with a weighted density approximation similar to the one used in the study of classical fluids, to phenomenologically account for short range correlations. After fixing the value of its parameters, the functional yields a good description of the equation of state and Landau parameters (spin symmetric and spin antisymmetric as well) from saturation to solidification densities. The zero sound propagation at finite momentum transfer is quantitatively reproduced up to the Fermi momentum, and qualitatively above it. The surface tension is in agreement with experiment, which makes the functional well suited for 3He drop calculations. We describe the structure of drops made of up to 516 atoms. As a novel application, we discuss the possible appearance of triplet pairing in a n/-shell of a drop, applying the formalism to the l j-shell holding up to 30 atoms from N = 169 to 198.

Motivated by the experimental finding of oddeven alternations in the mass spectra and ionization potentials of metal clusters, we have investigated the possibility of interpreting these results as evidence for pairing correlations among the electrons. For the present exploratory calculations, we have used a spherical BCS model which we have applied, as an example, to some A1 clusters. Additional model calculations have been carried out for NaN with 34 < N < 100 in order to illustrate a possible systematics. PACS: 74.20.Fg; 36.40. +d

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