Nucleus-Electron Model for States Changing from a Liquid Metal to a Plasma and the Saha Equation

TL;DR

This paper extends the QHNC method to model the transition of liquid rubidium into a plasma, accurately capturing electron correlations, ionization, and charge populations across a wide temperature range, and derives a high-density Saha equation.

Contribution

It introduces an extended QHNC approach to treat partially ionized plasmas and derives a Saha equation applicable to high-density, low-temperature conditions.

Findings

Liquid rubidium transitions from a liquid metal to plasma around 3 eV.

The method accurately predicts ionization levels and electron-ion correlations.

Charge populations are consistent with atomic structures across temperatures.

Abstract

We extend the quantal hypernetted-chain (QHNC) method, which has been proved to yield accurate results for liquid metals, to treat a partially ionized plasma. In a plasma, the electrons change from a quantum to a classical fluid gradually with increasing temperature; the QHNC method applied to the electron gas is in fact able to provide the electron-electron correlation at arbitrary temperature. As an illustrating example of this approach, we investigate how liquid rubidium becomes a plasma by increasing the temperature from 0 to 30 eV at a fixed normal ion-density $1.03 \times 10^{22}/cm^3$. The electron-ion radial distribution function (RDF) in liquid Rb has distinct inner-core and outer-core parts. Even at a temperature of 1 eV, this clear distinction remains as a characteristic of a liquid metal. At a temperature of 3 eV, this distinction disappears, and rubidium becomes a plasma with the ionization 1.21. The temperature variations of bound levels in each ion and the average ionization are calculated in Rb plasmas at the same time. Using the density-functional theory, we also derive the Saha equation applicable even to a high-density plasma at low temperatures. The QHNC method provides a procedure to solve this Saha equation with ease by using a recursive formula; the charge population of differently ionized species are obtained in Rb plasmas at several temperatures. In this way, it is shown that, with the atomic number as the only input, the QHNC method produces the average ionization, the electron-ion and ion-ion RDF's, and the charge population which are consistent with the atomic structure of each ion for a partially ionized plasma.