The Four-Boson System with Short-Range Interactions

Abstract

We consider the non-relativistic 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.

23 pages, revtex4, 5 PS figures, discussion expanded, results unchanged

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• Universality in Three- and Four-Body Bound States of Ultracold Atoms
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• Evidence for Universal Four-Body States Tied to an Efimov Trimer
• Universal Properties of the Four-Body System with Large Scattering Length
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• Scattering Models for Ultracold Atoms
• Universality and scaling limit of weakly-bound tetramers
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