Universal physics of bound states of a few charged particles

C.H. Schmickler (Institut für Kernphysik, Technische Universität Darmstadt, Darmstadt, Germany) ; H.W. Hammer (Institut für Kernphysik, Technische Universität Darmstadt, Darmstadt, Germany; ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany) ; A.G. Volosniev (Institut für Kernphysik, Technische Universität Darmstadt, Darmstadt, Germany; Institute of Science and Technology Austria, Klosterneuburg, Austria)

We study few-body bound states of charged particles subject to attractive zero-range/short-range plus repulsive Coulomb interparticle forces. The characteristic length scales of the system at zero energy are set by the Coulomb length scale D and the Coulomb-modified effective range reff. We study shallow bound states of charged particles with Dreff and show that these systems obey universal scaling laws different from neutral particles. An accurate description of these states requires both the Coulomb-modified scattering length and the effective range unless the Coulomb interaction is very weak (D). Our findings are relevant for bound states whose spatial extent is significantly larger than the range of the attractive potential. These states enjoy universality – their character is independent of the shape of the short-range potential.

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          "value": "ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum f\u00fcr Schwerionenforschung, Darmstadt, Germany"
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      "surname": "Volosniev", 
      "email": "artem.volosniev@ist.ac.at", 
      "full_name": "Volosniev, A.G.", 
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      "title": "Universal physics of bound states of a few charged particles"
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      "value": "We study few-body bound states of charged particles subject to attractive zero-range/short-range plus repulsive Coulomb interparticle forces. The characteristic length scales of the system at zero energy are set by the Coulomb length scale D and the Coulomb-modified effective range <math><msub><mrow><mi>r</mi></mrow><mrow><mi>eff</mi></mrow></msub></math>. We study shallow bound states of charged particles with <math><mi>D</mi><mo>\u226b</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>eff</mi></mrow></msub></math> and show that these systems obey universal scaling laws different from neutral particles. An accurate description of these states requires both the Coulomb-modified scattering length and the effective range unless the Coulomb interaction is very weak (<math><mi>D</mi><mo>\u2192</mo><mo>\u221e</mo></math>). Our findings are relevant for bound states whose spatial extent is significantly larger than the range of the attractive potential. These states enjoy universality \u2013 their character is independent of the shape of the short-range potential."
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Published on:
10 October 2019
Publisher:
Elsevier
Published in:
Physics Letters B , Volume 798 C (2019)

Article ID: 135016
DOI:
https://doi.org/10.1016/j.physletb.2019.135016
Copyrights:
The Authors
Licence:
CC-BY-3.0

Fulltext files: