An average atom code for warm matter: application to aluminum and uranium

Abstract

In astrophysics and in other sciences there is sometimes a need for information about the properties of matter, particularly equations of state, in extreme conditions of pressure and temperature. Global equation of state models, which represent solid, fluid and plasma states, typically consist of three parts: the cold curve, the ion-thermal contribution and the electron-thermal contribution. For the calculation of the latest part we present here an average atom embedded in a jellium code. We employ Liberman's relativistic and quantum model of matter which is a significant advance in complexity beyond the commonly used Thomas-Fermi model. We have applied specific algorithms to deal with the highly oscillatory nature of the free wavefunctions at high temperatures and to capture resonances which form in the continuum when bound states are destroyed by pressure ionization. Also we use massive parallel computing to treat the huge number of free wavefunctions at high temperatures (up to 10(9) K). Densities of states of resonant states are shown for uranium. With our code, which we have called Paradisio, we obtain tables of electron-thermal entropies from which free energies and pressures are derived. Our results are compared with those calculated in the Thomas-Fermi approximation and with available experiments. In aluminum, with our quantum code, a shell structure appears on the Hugoniot and a first-order metallic-nonmetallic transition is created at low densities and temperatures.