Energy-level structure of the hydrogen atom confined by a penetrable cylindrical cavity

Abstract

The bound-state energy spectrum and its evolution for a hydrogen atom located along the axis of a standard cylindrical confining cavity with either impenetrable or penetrable confining boundaries are obtained by solving the stationary Schrödinger equation using a finite differences approach. New results are first presented for a nuclear-centered position for the penetrable case as the barrier height and cavity size change. Special attention is then given to the energy-level dependence on the nuclear position along the cylinder axis, where proper identification for the evolution of states from the nuclear-centered position (centered states) up to the cylinder cap (cap states) is proposed, while the corresponding state evolution for intermediate nuclear positions (intermediate states) remains consistent with node conservation and symmetry. It is found that in general the energy levels evolve with an increasing value as the nuclear position is shifted from the central position up to a cylinder cap. As the barrier height (and cavity size) are reduced, a progressive extinction of bound states appears in the order cap states, intermediate states and centered states. Finally, a predominance of cavity-size over barrier-height effects on the energy level shift is found.

Ionisation and excitation probabilities of a hydrogen atom suddenly released from penetrable confinement

“…Refs. [1][2][3][4][5][6][7][8][9][10]. This has motivated a lot of interest in these systems for applications in different areas.…”

Recent progress in confined atoms and molecules: Superintegrability and symmetry breakings

“…(29)- (30), and the nuclear shielding factor, Eq. (31). Tables 2 and 3 report these asymptotic values compared also with precise numerical values and others by authors dealing with the same topics in the previous subsections 2.1.1, 2.1.2, 2.1.4 and 2.1.5, and its Refs.…”

“…On the other hand, the same Author in its Ref. [31] obtained expressions for the oscillator strength f 1s−2p , the ground state polarizability, Eqs. (29)- (30), and the nuclear shielding factor, Eq.…”

“…Table 2 shows the correlation energies estimated as the difference between the precise values of the energy, based on wave function expanded in a 40 Hylleraas basis set, and the HF energies of this work and its Refs. [30] and [31], as functions of the confining radius. The first two entries show that the correlation energy does not show appreciable changes in the third decimal figure.…”

“…"Energy-level structure of the hydrogen atom confined by a penetrable cylindrical cavity" [31] reports the boundstate energy spectrum and its evolution for the atom located along the axis of the cavity, with penetrable and impenetrable boundaries based on the solution of the Schrödinger equation using a finite difference approach. New results are presented for a nuclear centered position for the penetrable case as the barrier height and cavity size change.…”