Theory of plasmon interactions in an electron gas: Scattering of two plasmons

The interaction of two plasmons is calculated from first principles by two methods. Following the physical approach of Bohm and Pines, the scattering amplitude of two plasmons is dominated by the exchange of an electron-hole pair, although higher-order contributions yield minor quantitative corrections. The effective coupling between plasmons is found to be attractive and sufficiently strong to form a bound state of two plasmons at reasonably low electron densities (rs>3). An alternate derivation of the electron-plasmon Hamiltonian supports these conclusions. Possible extensions of the theory of systems of reduced dimensionality are briefly discussed in view of recently observed anomalies in the two-plasmon spectrum. © 1976 The American Physical Society.