Several sum rules and other exact relations are employed to determine both the static and the dynamic properties of strongly coupled, partially and completely degenerate one-component plasmas. Emphasis is placed on the electron gas, both at zero and finite temperatures. The procedure is based on the self-consistent method of moments, recently developed in Phys. Rev. Lett., 2017, 119, 045001, that provides a neat expression for the loss function valid at strong couplings. An input value of the method in its classical version is the static structure factor, whose accuracy is shown to insignificantly affect the resulting numerical data. Starting from the Cauchy-Bunyakovsky-Schwarz inequality, a criterion is proposed to verify the quality of various approaches to the evaluation of the static characteristics of one-component, strongly coupled plasmas.
KEYWORDSmethod of moments, static and dynamic structure factors, sum rules
INTRODUCTIONOne of the great challenges of modern plasma physics is the analytical and numerical description of the transition from collision-less to collision-dominated regimes in different Coulomb systems as well as of the crossover from classical to Fermi liquid behaviour of dense plasmas. [1,2] This is especially true for warm and hot dense matter or strongly coupled plasmas characterized by a wide range of variation of temperature T ∈ (10 4 -10 7 ) K and the mass density ∈ (10 −2 to 10 4 ) g/cm 3 , thereby spanning a few orders of magnitude variation. Within such a broad range of physical conditions, various effects compete with one another at different scales and impede the construction of bridging gap theories capable of predicting static and dynamic properties of systems under investigation. The above-stated domain of plasma parameters is, of course, of high relevance to inertial fusion devices, [3] but it is, nowadays, over-reached by other advanced laboratory studies as evidenced, for instance, in research on ultracold plasmas. [4] The focus of the present consideration is a one-component plasma that consists of a single particle species, say electrons, with the electric charge e, the mass m, and the number density n. The standard procedure is to introduce the following coupling and degeneracy parameters, respectively, as: Γ = e 2 /a and D = −1 = E F , where = (k B T) −1 denotes the inverse temperature in energy units, a = (4 n/3) −1/3 stands for the Wigner-Seitz radius, and E F = ℏ 2 (3 2 n) 2/3 /2m designates the Fermi energy. Another dimensionless quantity appropriate for the description of one-component plasma is the Brueckner parameter, defined as follows:
