Influence of shell effects on thermodynamic properties of matter at high pressures

Abstract

Abstract. We analyze the influence of shell effects on thermodynamic properties of matter at high pressures. Spherically symmetric average atom models show significant contribution of electronic transitions to cold pressure which is not confirmed by more accurate density functional theory models. In particular, the s-d transition in aluminum and potassium does not reveal itself on the shock Hugoniots. Oscillations on shock Hugoniots at very high pressures predicted earlier by many authors should be confirmed by precise first-principle calculations. IntroductionThermodynamic properties of matter at high pressure are of importance in many problems of high energy density physics, in particular, in astrophysics [1], in wide-range equations of state [2,3], in the problems of interaction of intense energy fluxes with matter [4-6], in perspective power generation facilities [7] and in some others. The finite-temperature Thomas-Fermi (TF) model [8] based upon semiclassical approximation is widely used to describe thermodynamic properties of matter, but there are many phenomena beyond this approach. In particular, shell effects reflect non-regularities of physical parameters because of the discrete energy spectrum. For example, in low-density plasma step-wise dependencies of thermodynamic functions on isochors or isobars are quite typical [9]. The other well-known effect is connected with the non-regular behavior of density of elements vs. atomic mass [10,11]. To describe shell effects one should take into account discrete energy levels. Analytically shell corrections to the TF model have been studied in [12,13] using the Poisson formula in the transition from summation to integration (see also the review [14]). Average atom models [15][16][17][18][19] are based on a radial solution of the single-particle Schrödinger (Dirac) equation so that the discrete spectrum and shell effects are taken into account implicitly. During the last 30 years it became possible to obtain approximate three-dimensional (3D) solutions of a quantum many-particle problem using density functional theory (DFT) [20,21]. In this case one gets a 3D band structure of a system of particles that provides for the appearance of shell effects through non-regularities of the electronic density and some thermodynamic functions. There were several attempts to register shell effects at high pressures and temperatures experimentally [22][23][24] using underground nuclear explosions. It is claimed [24] that the influence of the discrete energy spectrum is