# Cyclotron transitions of bound ions

## TL;DR

This paper investigates the quantum mechanical properties of bound complex ions in magnetic fields, revealing how their collective and internal motions influence cyclotron transitions differently from bare ions.

## Contribution

It introduces the concept of bound-ion cyclotron transitions, analyzing their energies and oscillator strengths with a rigorous quantum approach and deriving selection rules.

## Key findings

- Bound ions exhibit unique cyclotron transition energies.
- Coupling between collective and internal motions affects transition properties.
- Analytical and numerical methods are developed for transition analysis.

## Abstract

A charged particle in a magnetic field possesses discrete energy levels associated with particle's rotation around the field lines. The radiative transitions between these levels are the well-known cyclotron transitions. We show that a bound complex of particles with a non-zero net charge displays analogous transitions between the states of confined motion of the entire complex in the field. The latter {\em bound-ion cyclotron transitions} are affected by a coupling between the collective and internal motions of the complex and, as a result, differ from the transitions of a "reference" bare ion with the same mass and charge. We analyze the cyclotron transitions for complex ions by including the coupling within a rigorous quantum approach. Particular attention is paid to comparison of the transition energies and oscillator strengths to those of the bare ion. Selection rules based on integrals of collective motion are derived for the bound-ion cyclotron transitions analytically, and the perturbation and coupled-channel approaches are developed to study the transitions quantitatively. Representative examples are considered and discussed for positive and negative atomic and cluster ions.