Crossover behavior in a two-dimensional electron gas and quasiplasma oscillation

The dynamic structure factor for a two-dimensional (2D) electron gas at $T=0\mathrm{}$ is calculated by a method of recurrence relations. Our result indicates an interesting crossover behavior in going from interacting to noninteracting, which is unique to 2D electronic systems. The crossover behavior is characterized by a simple power law with a "classical" exponent, probably detectable by x rays. The validity of our result is tested against standard moment sum rules and also the static form-factor sum rule at high and low frequencies.