Pair Correlation Functions in Liquid Metallic Hydrogen

Abstract

The quantal hypernetted chain (QHNC) equation, derived from the Kohn-Sham-Mermin theory, is solved for the pair correlation functions in a liquid metallic hydrogen (LMH) modelled as a proton-electron mixture in the range where protons constitute a classical liquid and electrons are in a degenerate state. In the sufficiently high temperature and high density region, hydrogen atoms are found to form a metallic liquid where electrons have no bound state around a proton, and with decreasing temperature or density (for example, near rs=0.72 with the plasma parameter {Gamma}=100), an iterative process to solve the QHNC equation becomes unstable and diverges owing to the rapid growth in an attractive part of the effective electron-electorn interaction. In addition, it is shown that in the LMH there exists a first-order phase transition which is considered to cause a significant change in the electronic structure : At rs=0.3 and {Gamma}=20, for example, the QHNC equation has two sets of solutions belonging to two branches; the high temperature phase and the low temperature phase in which the distribution of electrons reflects more strongly the local order of protons.