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Four-Body Scale in Universal Few-Boson Systems

B. Bazak, J. Kirscher, S. König, M. Pavón Valderrama, N. Barnea, and U. van Kolck
Phys. Rev. Lett. 122, 143001 – Published 10 April 2019

Abstract

The role of an intrinsic four-body scale in universal few-boson systems is the subject of active debate. We study these systems within the framework of effective field theory. For systems of up to six bosons we establish that no four-body scale appears at leading order (LO). However, we find that at next-to-leading order (NLO) a four-body force is needed to obtain renormalized results for binding energies. With the associated parameter fixed to the binding energy of the four-boson system, this force is shown to renormalize the five- and six-body systems as well. We present an original ansatz for the short-distance limit of the bosonic A-body wave function from which we conjecture that new A-body scales appear at NA3 LO. As a specific example, calculations are presented for clusters of helium atoms. Our results apply more generally to other few-body systems governed by a large scattering length, such as light nuclei and halo states, the low-energy properties of which are independent of the detailed internal structure of the constituents.

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  • Received 2 December 2018
  • Revised 12 February 2019

DOI:https://doi.org/10.1103/PhysRevLett.122.143001

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & Optical

Authors & Affiliations

B. Bazak1, J. Kirscher2,3, S. König4,5, M. Pavón Valderrama6, N. Barnea1, and U. van Kolck7,8

  • 1The Racah Institute of Physics, The Hebrew University, 9190401, Jerusalem, Israel
  • 2Department of Physics, The City College of New York, New York, New York 10031, USA
  • 3Theoretical Physics Division, School of Physics and Astronomy, The University of Manchester, Manchester, M13 9PL, United Kingdom
  • 4Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt, Germany
  • 5ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany
  • 6School of Physics and Nuclear Energy Engineering, International Research Center for Nuclei and Particles in the Cosmos and Beijing Key Laboratory of Advanced Nuclear Materials and Physics, Beihang University, Beijing 100191, China
  • 7Institut de Physique Nucléaire, CNRS-IN2P3, Université Paris-Sud, Université Paris-Saclay, 91406 Orsay, France
  • 8Department of Physics, University of Arizona, Tucson, Arizona 85721, USA

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Issue

Vol. 122, Iss. 14 — 12 April 2019

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