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arXiv:1109.5807 · Physical Review A

Universality and the three-body parameter of 4 He trimers

Pascal Naidon, Emiko Hiyama, Masahito Ueda

Published Jul 9, 2012• 43 citations
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Abstract

We consider a system of three ${}^{4}$He atoms, which is so far the simplest realistic three-body system exhibiting the Efimov effect, in order to analyze deviations from the universal Efimov three-body spectrum. We first calculate the bound states using a realistic two-body potential, and then analyze how they can be reproduced by simple effective models beyond Efimov's universal theory. We find that the nonuniversal variations of the ground and first excited states can be well reproduced by models parametrized with only three quantities: the scattering length and effective range of the original potential, and a small three-body force. Furthermore, the three-body parameter, which fixes the origin of the infinite set of three-body levels, is found to be consistent with recent experimental observations in other atomic species.

DOI
10.1103/physreva.86.012502

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Three- and four-boson systems expanded around the unitarity limit: Application to 4^44He molecules
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Efimov states are a sequence of shallow three-body bound states that arise when the two-body scattering length is large. Efimov showed that the binding energies of these states can be calculated in terms of the scattering length and a three-body parameter by solving a transcendental equation involving a universal function of one variable. We calculate this universal function using effective field theory and use it to describe the three-body system of 4He{}^{4}\mathrm{He}4He atoms. We also extend Efimov's theory to include the effects of deep two-body bound states, which give widths to the Efimov states.