Equation of motion for a bound system of charged particles

TL;DR

This paper derives a comprehensive equation of motion for a bound system of charged particles with polarizabilities in an external electromagnetic field, accounting for relativistic effects and internal degrees of freedom.

Contribution

It introduces a bound-continuum perturbation theory to accurately describe the motion of polarizable bound systems like atoms and nuclei.

Findings

Derived a complete formula for the equation of motion.

Highlighted the importance of polarizabilities in high-precision applications.

Addressed the challenge of defining polarizability in continuum spectra.

Abstract

We consider a bound system of charged particles moving in an external electromagnetic field, including leading relativistic corrections. The difference from the point particle with a magnetic moment comes from the presence of polarizabilities. Due to the lack of separation of the total momentum from the internal degrees of freedom, the notion of polarizability of the bound state immersed in the continuum spectrum of the global motion is nontrivial. We introduce a bound-continuum perturbation theory and obtain a complete formula for the equation of motion for a polarizable bound system, such as atom, ion, or the nucleus. This formula may find applications when high precision is sought and small effects due polarizabilities are important.