Theoretical model of x-ray scattering as a dense matter probe

Abstract

We present analytical expressions for the dynamic structure factor, or form factor S(k,omega), which is the quantity describing the x-ray cross section from a dense plasma or a simple liquid. Our results, based on the random phase approximation for the treatment on the charged particle coupling, can be applied to describe scattering from either weakly coupled classical plasmas or degenerate electron liquids. Our form factor correctly reproduces the Compton energy down-shift and the known Fermi-Dirac electron velocity distribution for S(k,omega) in the case of a cold degenerate plasma. The usual concept of scattering parameter is also reinterpreted for the degenerate case in order to include the effect of the Thomas-Fermi screening. The results shown in this work can be applied to interpreting x-ray scattering in warm dense plasmas occurring in inertial confinement fusion experiments or for the modeling of solid density matter found in the interior of planets.

Inelastic X-Ray Scattering from Shocked Liquid Deuterium

“…An easier fourth-order interpolation between the classical Debye length and the Thomas-Fermi screening length valid for T = 0 yields the correct results within 2% [19]. If α s < 1, the scattering is dominated by independent electrons and is referred to as noncollective [12]. In this case, the free-electron contribution experiences a significant…”

“…inelastic x-ray scattering a powerful diagnostic providing electron temperature (T e ), electron density (n e ), and ionization (Z) for critical EOS measurements in ICF and planetary science research [10][11][12][13][14].…”

The effect of bound states on X-ray Thomson scattering for partially ionized plasmas

“…The electron-electron contribution S ee (k,ω) is expressed in terms of the dielectric function ε(k,ω) of the free electrons, which in turn is evaluated using the random-phase approximation (RPA) as in Ref. [2]. Finally, bound-state contributions to the dynamic structure function are evaluated using average-atom bound-and continuum-state wave functions, with the latter approaching plane waves asymptotically.…”

“…The theoretical model developed by Gregori et al [2] is used to evaluate the ion-ion contribution S ii (k,ω) to the dynamic structure function, with scattering form factors (Fourier transforms of the charge densities) calculated with bound-and continuum-state wave functions from our average-atom code. Additionally, the procedure proposed in Ref.…”

“…We start with the theoretical model proposed by Gregori et al [2] but evaluate the Thomsonscattering dynamic structure function using parameters taken from our own average-atom code [3,4]. The average-atom model is a quantum mechanical version of the temperature-dependent Thomas-Fermi model of plasma developed years ago by Feynman et al [5].…”