Abstract
In this paper we study the phase diagram of the ground-state quantum numbers as functions of Haldane pseudopotential parameters ${\mathit{V}}_{0}$ and ${\mathit{V}}_{1}$, keeping all other ${\mathit{V}}_{\mathit{m}}$'s at their Coulomb values. We study filling factors 1/2 and 5/2, using a system of eight electrons on a sphere. It is known that the Coulomb ground state is not a spin singlet. In the phase diagram, however, we find that there is a comparatively large region of L=0, S=0 states not far from the Coulomb point. Modifications necessary for the ground state to be in this sector are discussed. Some of the L=0, S=0 states in the phase diagram are incompressible because they have significant overlaps with the hollow core state or with the composite fermion states, which are known to be imcompressible.
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