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

We consider the correlation between the binding energies of the triton and the α-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 α-particle. We calculate this correlation and obtain a prediction for the α-particle binding energy. Corrections to our results are suppressed by ℓ/|a|.