Parametric instabilities in quantum plasmas with electron exchange-correlation effects

Parametric instabilities induced by the nonlinear interaction between high frequency quantum Langmuir waves and low frequency quantum ion-acoustic waves in quantum plasmas with the electron exchange-correlation effects are presented. By using the quantum hydrodynamic equations with the electron exchange-correlation correction, we obtain an effective quantum Zaharov model, which is then used to derive the modified dispersion relations and the growth rates of the decay and four-wave instabilities. The influences of the electron exchange-correlation effects and the quantum effects on the existence of quantum Langmuir waves and the parametric instabilities are discussed in detail. It is shown that the electron exchange-correlation effects and quantum effects are coupled strongly. The quantum Langmuir wave can propagate in quantum plasmas only when the electron exchange-correlation effects and the quantum effects satisfy a certain condition. The electron exchange-correlation effects tend to enhance the parametric instabilities, while quantum effects suppress the instabilities.