``Fermi Liquid'' Shell Model Approach to Composite Fermion Excitation Spectra in Fractional Quantum Hall States

Abstract

Numerical results for the energy spectra of $N$ electrons on a spherical surface are used as input data to determine the quasiparticle energies and the pairwise ``Fermi liquid'' interactions of composite Fermion (CF) excitations in fractional quantum Hall systems. The quasiparticle energies and their interactions are then used to determine the energy spectra, $E$ vs total angular momentum $L$, of states containing more than two quasiparticles. The qualitative agreement with the numerical results gives a remarkable new confirmation of the CF picture.