INTERACTION OF QUASI-PARTICLES IN THE 1/3 QUANTUM HALL STATE AND HIERARCHICAL ESTIMATES OF THE ENERGY OF DAUGHTER STATES

The interaction of quasiparticles in the 1/3 state is determined by exact calculations using systems with up to nine electrons. Within the hierarchical scheme proposed by Halperin, which is based on quasiparticles obeying fractional statistics, we use these results to estimate the energies and gaps of the polarized and unpolarized 2/5 states and of the polarized and partially polarized 4/11 states. Our results confirm the ability of the hierarchical scheme to provide accurate quantitative estimates for the fractional states issuing from the 1/3 state.