Multicomponent dense electron gas as a model of Si MOSFET

We solve a 2D model of N-component dense electron gas in the limit N→∞ and in the range of the Coulomb interaction parameter N ^?3/2?r _s ?1. The quasiparticle interaction on the Fermi circle vanishes as ?²/Nm. The ground-state energy and the effective mass are found as series in powers of r _s ^2/3 . In the quantum Hall state on the lowest Landau level at integer filling 1?ν<N, the charge-activation-energy gap and the exchange constant are Δ=log(r _s N^3/2)?ω_H/ν and J=0.66?ω_H/ν.