Metallization in hydrogenlike systems under high pressure

Abstract

Almost a century ago, it was proposed that solid hydrogen could become metallic at sufficiently high pressure. Five years back, scientists observed an insulator to metal transition in liquid deuterium experimentally, at around 300 $\mathrm{GPa}$. The present work discusses and demonstrates the metal-like behavior in elemental hydrogen under various plasma environments. At the onset, the Herzfeld criterion is invoked to examine such characteristics in such plasmas under multimegabar pressure. However, a thorough study using this condition can only explain the metal-like pattern in $s$-wave states under a shell-confined condition (the system is trapped inside two concentric spheres with inner and outer radii ${R}_{a},{R}_{b}$). Moreover, using this criterion, it is not possible to explain such phenomena in (i) confined systems (involving all $\ensuremath{\ell}$) and (ii) for $\ensuremath{\ell}\ensuremath{\ne}0$ states in a shell-confined environment. Here this criterion is modified to incorporate the environmental conditions (nuclear charge, screening constant, boundary conditions) by utilizing several independent and generalized scaling concepts. The present condition can interpret a metallic pattern in confined and shell-confined plasmas connecting $\ensuremath{\ell}\ensuremath{\ge}0$ states. Further, a different descriptor is proposed therefrom. The role of pressure in defining such a descriptor is also examined. Pilot calculations are performed using Debye H\"uckel, exponential screen Coulomb potential, and ion-sphere plasmas. The relevance of the shell-confined model in the context of plasmas is elaborated. Additionally, an attempt is made to investigate the metallic character in H-like systems embedded in fullerene under high pressure.