  Two- and three-body correlations in partially filled degenerate fermion
shells are studied numerically for various interactions between the particles.
Three distinct correlation regimes are defined, depending on the short-range
behavior of the pair pseudopotential. For pseudopotentials similar to those of
electrons in the first excited Landau level, correlations at half-filling have
a simple three-body form consisting of the maximum avoidance of the triplet
state with the smallest relative angular momentum R_3=3. In analogy to the
superharmonic criterion for Laughlin two-body correlations, their occurrence is
related to the form of the three-body pseudopotential at short range. The
spectra of a model three-body repulsion are calculated, and the zero-energy
Moore--Read ground state, its +-e/4-charged quasiparticles, and the
magnetoroton and pair-breaking bands are all identified. The quasiparticles are
correctly described by a composite fermion model appropriate for Halperin's
p-type pairing with Laughlin correlations between the pairs. However, the
Moore--Read ground state, and specially its excitations, have small overlaps
with the corresponding Coulomb eigenstates when calculated on a sphere. The
reason lies in surface curvature which affects the form of pair pseudopotential
for which the "R_3>3" three-body correlations occur. In finite systems, such
pseudopotential must be slightly superharmonic at short range (different from
Coulomb pseudopotential). However, the connection with the three-body
pseudopotential is less size-dependent, suggesting that the Moore--Read state
and its excitations are a more accurate description for experimental nu=5/2
states than could be expected from previous calculations.
