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The trial wave function method developed in Ref.s \cite{gutz,brink} for thecase of narrow {\it s}-band in a perfect crystal is adapted for calculation ofthe density dependence of the effective mass and the Lande factor in a dilutetwo-dimensional electron system. We find that the effective mass has a tendencyto diverge at a certain critical concentration, whereas the $g$ factor remainsfinite.Comment: 5 pages, 2 figures. Published in JETP Letter

On effective electron mass of silicon field structures at low electron densities