A solvable model for decoupling of interacting clusters

¹ Institut für Kernphysik, Technische Universität Darmstadt - 64289 Darmstadt, Germany
² Department of Physics and Astronomy, Aarhus University - DK-8000 Aarhus C, Denmark
³ Department of Physics, American University - 4400 Massachusetts Ave. NW, Washington, DC 20016, USA
⁴ Department of Physics and Astronomy, University of Nebraska at Kearney - 2401 11th Avenue Kearney, NE 68849, USA
⁵ Aarhus Institute of Advanced Studies, Aarhus University - DK-8000 Aarhus C, Denmark

Received: 29 October 2018
Accepted: 10 January 2019

Abstract

We consider M clusters of interacting particles, whose in-group interactions are arbitrary, and inter-group interactions are approximated by oscillator potentials. We show that there are masses and frequencies that decouple the in-group and inter-group degrees of freedom, which reduces the initial problem to M independent problems that describe each of the relative in-group systems. The dynamics of the M center-of-mass coordinates is described by the analytically solvable problem of M coupled harmonic oscillators. This letter derives and discusses these decoupling conditions. Furthermore, to illustrate our findings, we consider a charged impurity interacting with a ring of ions. We argue that the impurity can be used to probe the center-of-mass dynamics of the ions.