Discontinuities in Acoustic Parametric Processes in a Degenerate Electron Gas

Calculations and experimental results are presented on the nonlinear part of the interaction of free electrons with acoustic phonons which gives rise to acoustic sum-frequency generation. For a degenerate electron gas, the nonlinearity increases discontinuously at $\left|{\overrightarrow{\mathrm{q}}}_3\right|=2\mathrm{}{k}_{\mathrm{F}}$, where ${\overrightarrow{\mathrm{q}}}_3$ is the acoustic wave vector at the sum frequency and $k_{\mathrm{F}}$ is the electron Fermi wave vector. This abrupt increase was observed in GaAs using x-ray scattering.