Plasmon dispersion in the local-density approximation

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Abstract
The plasmon dispersion relation omega q is calculated including correlation and inhomogeneity corrections of the valence electrons. By using the local-density approximation the correlation problem is reduced to that in the homogeneous system. The author's theory allows him to circumvent completely the problem of local-field corrections (originating from off-diagonal elements of the dielectric matrix). For weakly inhomogeneous systems the coefficients of the expansion omega q= omega 0+ alpha q2+. . . are expressed by two parameters: (i) the mean-square deviation of the valence charge density ( Delta n)2=n2-n2 and (ii) a parameter zeta , which introduces correlations into the parameter alpha 0 of a homogeneous system and which is defined by alpha 0/ alpha 0,RPA=1- zeta rs. Numerical results for several metals and semiconductors are presented and compared with experiment.