Shell-confined atom and plasma: incidental degeneracy, metallic character and information entropy

TL;DR

This paper explores shell-confined hydrogen-like atoms, revealing incidental degeneracies, metallic behavior, and information entropy characteristics, with new analytical expressions and implications for plasma systems.

Contribution

It introduces a comprehensive analysis of shell-confined atoms, uncovering incidental degeneracies, evaluating oscillator strengths and polarizabilities, and examining information entropy in confined quantum systems.

Findings

Incidental degeneracy arises at specific shell confinements.

Negative polarizability observed in excited states.

Analytical expressions derived for oscillator strengths and polarizabilities.

Abstract

Shell confined atom can serve as a generalized model to explain both \emph{free} and \emph{confined} condition. In this scenario, an atom is trapped inside two concentric spheres of inner $(R_{a})$ and outer $(R_{b})$ radius. The choice of $R_{a}, R_{b}$ renders four different quantum mechanical systems. In hydrogenic atom, they are termed as (a) free hydrogen atom (FHA) (b) confined hydrogen atom (CHA) (c) shell-confined hydrogen atom (SCHA) (d) left-confined hydrogen atom (LCHA). By placing $R_{a}, R_{b}$ at the location of radial nodes of respective \emph{free} $n,\ell$ states, a new kind of degeneracy may arise. At a given $n$ of FHA, there exists $\frac{n(n+1)(n+2)}{6}$ number of iso-energic states with energy $-\frac{Z^{2}}{2n^{2}}$. Furthermore, within a given $n$, the individual contribution of each of these four potentials has also been enumerated. This incidental degeneracy concept is further explored and analyzed in certain well-known \emph{plasma} (Debye and exponential cosine screened) systems. Multipole oscillator strength, $f^{(k)}$, and polarizability, $\alpha^{(k)}$, are evaluated for (a)-(d) in some low-lying states $(k=1-4)$. In excited states, \emph{negative} polarizability is also observed. In this context, metallic behavior of H-like systems in SCHA is discussed and demonstrated. Additionally analytical closed-form expression of $f^{(k)}$ and $\alpha^{(k)}$ are reported for $1s,2s,2p,3d,4f,5g$ states of FHA. Finally, Shannon entropy and Onicescu {\color{red}information} energies are investigated in ground state in SCHA and LCHA in both position and momentum spaces. Much of the results are reported here for first time.