Evolution of atomic optical selection rules upon gradual symmetry lowering

TL;DR

This paper analyzes how optical selection rules in atoms change as symmetry is gradually distorted, combining analytical and numerical methods to reveal the evolution from circular to linear transition characters.

Contribution

It provides a detailed analysis of the continuous evolution of optical selection rules under symmetry distortion using a hydrogen atom model with environmental charges.

Findings

Selection rules evolve from circular to linear with increasing distortion

Allowed and forbidden transitions interchange as symmetry is lowered

Analytical and numerical results illustrate the evolution process

Abstract

For atoms and crystals with an ideal symmetry, the optical selection rules for electronic transitions are well covered in physics textbooks. However, in studies of material systems one often encounters systems with a weakly distorted symmetry. Insight and intuition for how optical selection rules change when an ideal symmetry is gradually distorted is, nevertheless, little addressed in literature. We present here a detailed analysis of how a gradual symmetry distortion leads to a complete alteration of optical selection rules. As a model system, we consider the transitions between $1s$ and $2p$ sublevels of the hydrogen atom, which get distorted by placing charged particles in its environment. Upon increasing the distortion, part of the optical selection rules evolve from circular via elliptical to linear character, with an associated evolution between allowed and forbidden transitions. Our presentation combines an analytical approach with quantitative results from numerical simulations, thus providing insight in how the evolution occurs as a function of the strength of the distortion.