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Phys. Rev. A 70, 052101 (2004) [13 pages]

Four-boson system with short-range interactions

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L. Platter*
Forschungszentrum Jülich, Institut für Kernphysik, D-52425 Jülich, Germany and Helmholtz-Institut für Strahlen-und Kernphysik (Theorie), Universität Bonn, Nussallee 14-16, D-53115 Bonn, Germany

H.-W. Hammer†
Institute for Nuclear Theory, University of Washington, Seattle, Washington 98195, USA

Ulf-G. Meißner‡
Helmholtz-Institut für Strahlen-und Kernphysik (Theorie), Universität Bonn, Nussallee 14-16, D-53115 Bonn, Germany and Forschungszentrum Jülich, Institut für Kernphysik, D-52425 Jülich, Germany

Received 15 April 2004; revised 2 July 2004; published 5 November 2004

We consider the nonrelativistic four-boson system with short-range forces and large scattering length in an effective quantum mechanics approach. We construct the effective interaction potential at leading order in the large scattering length and compute the four-body binding energies using the Yakubovsky equations. Cutoff independence of the four-body binding energies does not require the introduction of a four-body force. This suggests that two- and three-body interactions are sufficient to renormalize the four-body system. We apply the equations to 4He atoms and calculate the binding energy of the 4He tetramer. We observe a correlation between the trimer and tetramer binding energies similar to the Tjon line in nuclear physics. Over the range of binding energies relevant to 4He atoms, the correlation is approximately linear.

© 2004 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevA.70.052101
DOI:
10.1103/PhysRevA.70.052101
PACS:
03.65.Ge, 36.40.−c, 21.45.+v

*Electronic address: l.platter@fz-juelich.de

†Electronic address: hammer@phys.washington.edu

‡Electronic address: meissner@itkp.uni-bonn.de

 
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