Calculation of the Dynamic Structure Factor of Model Coulomb Systems using the Method of Moments and Effective Potentials

Classical MD data on the dynamic charge-charge structure factor Szz(k, ω) of semi-quantal hydrogen plasmas modelled in [1] are revisited using the sum rules and other exact relations to reconstruct the system loss function, and the method of effective potentials to estimate its static characteristics. Introduction Classical molecular dynamics (MD) simulations of model hydrogen plasmas were carried out in [1] twenty five years ago. Quantum effects preventing the collapse were taken into account through the use of the Deutsch pair micropotential [2] arising from the quantum-diffraction effects. Our aim here is to reexamine the simulation data of [1] within the moment approach and using the method of effective potentials to estimate the static characteristics of the TCP. The convergent power moments [3] of the loss function −Imε(k, ω)/ω of the model system can be expressed in terms of its partial static structure factors and the latter are computed by the method of hypernetted chains using the Deutsch effective potential as the micropotential. In addition, a new model for the Nevanlinna parameter function is suggested and tested. The classical fluctuationdissipation theorem with the Nevanlinna formula of the classical theory of moments expresses the response function [3] ε(k, z) in terms of a Nevanlinna class function Q = Q(k, z), analytic in the upper half-plane Imz > 0 and possessing there a positive imaginary part: ImQ(k, ω + iη) > 0, η > 0, the function Q(k, z) should also satisfy the limiting condition limz→∞ Q(k, z)/z = 0, Imz > 0. The Nevanlinna function model It is easy to see that due to the Kramers-Kronig relations the asymptotic expansion of the inverse dielectric function is determined by the moments Cν (k), ν = 2, 4: ε(k, z → ∞) ' 1 + C2 (k) z + C4 (k) z + o (