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On the correlation between the binding energies of the triton and the alpha-particle

L. Platter·H. -W. Hammer·U. -G. Meißner
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Abstract

We consider the correlation between the binding energies of the triton and the alpha-particle which is empirically observed in calculations employing different phenomenological nucleon-nucleon interactions. Using an effective quantum mechanics approach for short-range interactions with large scattering length |a| >> l, where l is the natural low-energy length scale, we construct the effective interaction potential at leading order in l/|a|. In order to renormalize the four-nucleon system, it is sufficient to include a SU(4)-symmetric one-parameter three-nucleon interaction in addition to the S-wave nucleon-nucleon interactions. The absence of a four-nucleon force at this order explains the empirically observed correlation between the binding energies of the triton and the alpha-particle. We calculate this correlation and obtain a prediction for the alpha-particle binding energy. Corrections to our results are suppressed by l/|a|.

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L. Platter, H. -W. Hammer, U. -G. Meißner. 2004-11-22. On the correlation between the binding energies of the triton and the alpha-particle. https://doi.org/10.1016/j.physletb.2004.12.068

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