---
abstract: 'A presentation and a generalisation are given of the phenomenon of level rearrangement, which occurs when an attractive long-range potential is supplemented by a short-range attractive potential of increasing strength. This problem has been discovered in condensate-matter physics and has also been studied in the physics of exotic atoms. A similar phenomenon occurs in a situation inspired by quantum dots, where a short-range interaction is added to an harmonic confinement.'
author:
- Monique Combescure
- Avinash Khare
- Ashok Raina
- 'Jean-Marc Richard'
- Carole Weydert
title: Level rearrangement in exotic atoms and quantum dots
---

Introduction
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In 1959, Zel’dovich [@Zel59] discovered an interesting phenomenon while considering an excited electron in a semi-conductor. The model describing the electron–hole system consists of a Coulomb attraction modified at short-distance [@kolomeisky:022721]. A similar model is encountered in the physics of exotic atoms: if an electron is substituted by a negatively-charged hadron, this hadron feels both the Coulomb field and the strong interaction of the nucleus. The Zel’dovich effect has also been discussed for atoms in a strong magnetic field [@Karnakov].

Zel’dovich [@Zel59] and later Shapiro and his collaborators [@Kudryavtsev:1978af; @Shapiro:1978wi] look at how the atomic spectrum evolves when the strength 