An α-particle model for ¹⁶O: Is there a new four-body scale?

The ¹⁶O nucleus is modelled as a system of four α-particles. It is shown that a Hamiltonian that includes established two- and three-body forces reproducing the α-α phase shifts, the ⁸Be resonance, and the first and second 0⁺ states of ¹²C overbinds the ¹⁶O nucleus. To rectify this a novel four-body force is introduced, which then leads to a good agreement with the low-lying experimental spectrum of ¹⁶O.