Phonon Contribution to the Dynamic Form Factor of the Electrons in Metals

H. Hinkelmann
1975 Zeitschrift fur Naturforschung A-A Journal of Physical Sciences  
For a metal a simple relation between the dynamical form factors Sei (9, <*>) and Sion(9< ( -q, 0)) (<%i(q, t)) . The second and third term on the r.h.s. of (4) do no longer depend on t. We are now going to approximate the first term. Let us consider the vibrating ions of a metal as external charges that perturb the density of the conduction electrons. The linear response of the electrons to this perturbation is then given by (AQlp(q,) is the Fourier-transform of the ion density change due to
more » ... ity change due to the displacement oif the ions from their equilibrium positions Approximating the first term on the r.h.s. of (4) with (5) we finally get for (2) Sel{q,co) =S°el(q,w) + £0{q,oj) -1 F(q)\ 2 Sion(q, co) +C(q)d(oj). (7) C{q) results from the constant terms under the integral in (2). We need not know the difinite expression of it for further considerations.
doi:10.1515/zna-1975-0120 fatcat:4yrraq3f7rdd7pbfehj3i6xkm4