Scattering of Light by Light in Plasmas

A quantum-mechanical calculation of the scattering rate of light by light in the polarizable medium of a plasma is carried out. It is shown that if the frequency ${\omega }_0$ of the incident light is much greater than the electron plasma frequency ${\omega }_p$, the $\rho A^2$ term in the nonrelativistic Hamiltonian coupling the radiation to matter dominates the j.A interaction, provided the frequency shifts $\Delta \omega$ satisfy $\Delta \omega \ll {\omega }_0$. In this approximation, the scattering amplitude is proportional to the Green's function for electron-density fluctuations (which reduces to the electron-density correlation function in the classical limit). This leads to an expression for the differential scattering rate which is formally exact to all orders in the interparticle interactions. The spectrum of the scattered light in this approximation has resonances at the collective modes of the plasma if $\frac{{\omega }_0}{c}\ll k_D$, the Debye wave number. The total scattering rate is estimated in the collisionless (random-phase) approximation. Under the conditions of this calculation, rather high plasma densities and temperatures are required to obtain a detectable rate.