Perturbation theory for confined systems

TL;DR

This paper explores the use of perturbation theory to analyze particles confined in a spherical box, demonstrating near-independence under strong confinement and applying the method to a helium atom with a moving nucleus.

Contribution

It introduces a perturbation approach for confined systems and compares moving versus fixed nucleus models, explaining recent numerical findings.

Findings

Particles behave almost independently under strong confinement

First-order results align with numerical data for helium atom

Moving nucleus model provides insights into confinement effects

Abstract

We discuss the application of perturbation theory to a system of particles confined in a spherical box. A simple argument shows that the particles behave almost independently in sufficiently strong confinement. We choose the helium atom with a moving nucleus as a particular example and compare results of first order with those for the nucleus clamped at the center of the box. We provide a suitable explanation for some numerical results obtained recently by other authors.