A DENSITY-FUNCTIONAL FOR LIQUID-HE-3

We present a density functional for the description of liquid He-3 pro perties at zero temperature in a mean field approximation. Its basic i ngredients are a zero-range, particle- and spin-density dependent effe ctive interaction of Skyrme type, and a long-range effective interacti on of Lennard-Jones type supplemented with a weighted density approxim ation similar to the one used in the study of classical fluids, to phe nomenologically 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 a ntisymmetric 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 s urface tension is in agreement with experiment, which makes the functi onal well suited for He-3 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 nl-shell of a drop, ap plying the formalism to the 1j-shell holding up to 30 atoms from N = 1 69 to 198.