Spectroscopic properties of an isotropically compressed hydrogen atom

Abstract

We use a numerical solution of the Schrodinger equation for a hydrogen atom at the center of an inert, impenetrable, spherical cavity, to predict the influence of isotropic compression on spectroscopic properties. The angular momentum sublevel degeneracy that occurs for the free atom is removed under isotropic compression. We account for this splitting on the basis of the underlying distribution functions. We find that the principal lines in the Lyman and Balmer series are blue-shifted relative to the free-atom frequencies, but, depending on the cavity radius, the intensities of these lines can be either enhanced or diminished, relative to the free atom intensities. We find that the excited-state lifetimes are all reduced by compression, with the reduction being especially large for the 2s level. We also find that nuclear volume effects on the electronic energy are greatly enhanced by isotropic compression.

Confined systems and the modified virial theorem from semiclassical considerations

“…The energies of isotropically compressed hydrogenic orbitals follow similar trends as functions of R (see, e.g., figure 2 of Ref. [6]). On the other hand, one can study the behavior of (n) as a function of n, keeping L fixed.…”

Calculated Electronic Behavior and Spectrum of Mg+@C60 Using a Simple Jellium-shell Model

“…However, some relevant recent works on confined hydrogen -the most simple system to study theoretically -nicely compliment the earliest papers [4,5]. For example, variational perturbation theory is used to study the positional behavior of confined H [14] and a numerical solution to Schrödinger's Equation is employed to examine the behavior of confined H which is isotropically compressed [15]. In the interest of better understanding the behavior of species encapsulated within Fullerenes, a jellium shell model has been used in a recent study of the behavior of H confined at the center of a deformable cage [16], showing outstanding agreement with experiment and other theoretical results.…”

Calculation of Atomic Structure

“…The effect of applied pressure on the electronic structure of the hydrogen atom has been studied many times [20,21] by changing the boundary condition in wavemechanical simulation of the energy-level structure. The general effect is an increase of all energy levels with pressure, until the point is reached where the ground-state level reaches the ionization limit on compression to a radius of r 0 = 1.835a 0 .…”