Plasmon damping in the free-electron gas model of solids

We address the problem of quantifying the decay of plasmons excited in the electron gas of a condensed medium. Within the dielectric formalism, we thoroughly describe the theoretical framework in which we define the damping parameter $\gamma$. We present two detailed procedures to assess it as a function of the momentum transfer q, one based on a classical description of the excitation process and the second based on a quantum formulation of it. We present results corresponding to aluminum and magnesium, and compare them with experimental data obtained from the literature.