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

Abstract

Shell confined atom can serve as a generalized model to explain both free and 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 free n, ℓ states, a new kind of degeneracy may arise.At a given n of FHA, there exists n(n+1)(n+2) 6 number of iso-energic states with energy − 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 plasma (Debye and exponential cosine screened) systems. Multipole oscillator strength, f (k) , and polarizability, α (k) , are evaluated for (a)-(d) in some low-lying states (k = 1 − 4). In excited states, 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 α (k) are reported for 1s, 2s, 2p, 3d, 4f, 5g states of FHA. Finally, Shannon entropy and Onicescu 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.