Plasmon Dispersion in Lithium for Large Wave Vectors

Using Bohm‐Pines Hamiltonian for the electron‐plasmon system the one plasmon propagator is evaluated, the poles of which determine the plasmon frequency. It is found that the interaction term bilinear in the plasmon coordinates mostly give rise to a negative shift to the classical plasma frequency ω p l at k = 0. Redefining the critical wave vector k c used in the random phase approximation (RPA) the observed plasmon frequency of ≈ 0.9 ω p l at k = 0 in Li is reproduced. The new critical wave vector is found to be much larger than k   c RPAimplying that the plasmons continue to exist beyond k   C RPA . The calculations for the dynamic structure factor corresponding to the plasmon excitations, S p l( k , ω), show that this has a Gaussian form for momentum transfer larger than ≈ 0.4 k F . Adding to this the dynamic structure factor for the quasi‐particle excitations, it is possible to observe a structure in the total S ( k , ω) near k ≈ k   c RPA . The plasmon dispersion and line‐width estimated from the theory for Li are found to agree fairly well with those of the experiments.