Dielectric tensor and shear-mode dispersion for strongly coupled Coulomb liquids: Three-dimensional one-component plasmas

We analyze the transverse dielectric response function and the collective excitations in a strongly coupled one-component plasma (OCP). The collective modes are either photonlike or phononlike. The latter, which are maintained by shear, are unique to the strongly coupled system. We employ the recently established quasilocalized-charge model to develop a theory of the shear mode in the strongly coupled OCP. We examine in detail the dispersion of the shear mode in the 20${\mathit{Z}}^2$${\mathit{e}}^2$/${\mathit{ak}}_{\mathit{B}}$T, a is the Wigner-Seitz radius), and compare it with the result of molecular-dynamics simulations of Hansen, McDonald, and Pollock [Phys. Rev. A 11, 1025 (1975)]. The agreement between the theory and the simulation results is quite satisfactory in the low-k domain, but the theory is unable to account for the observed high-k splitting of the shear mode. We also establish the correspondence between the shear mode of the strongly coupled OCP liquid and the acoustic phonons of the Wigner crystal.