  The mean field composite Fermion (CF) picture successfully predicts angular
momenta of multiplets forming the lowest energy band in fractional quantum Hall
(FQH) systems. This success cannot be attributed to a cancellation between
Coulomb and Chern-Simons interactions beyond the mean field, because these
interactions have totally different energy scales. Rather, it results from the
behavior of the Coulomb pseudopotential V(L) (pair energy as a function of pair
angular momentum) in the lowest Landau level (LL). The class of short range
repulsive pseudopotentials is defined that lead to short range Laughlin like
correlations in many body systems and to which the CF model can be applied.
These Laughlin correlations are described quantitatively using the formalism of
fractional parentage. The discussion is illustrated with an analysis of the
energy spectra obtained in numerical diagonalization of up to eleven electrons
in the lowest and excited LL's. The qualitative difference in the behavior of
V(L) is shown to sometimes invalidate the mean field CF picture when applied to
higher LL's. For example, the nu=7/3 state is not a Laughlin nu=1/3 state in
the first excited LL. The analysis of the involved pseudopotentials also
explains the success or failure of the CF picture when applied to other systems
of charged Fermions with Coulomb repulsion, such as the Laughlin quasiparticles
in the FQH hierarchy or charged excitons in an electron-hole plasma.
