Three body resonances in a coupled channel ND approach

Assuming a three body channel to be dominated by the formation of bound states and resonances, the three body problem is reduced to an effective two body coupled channel problem in which pairs of particles, either bound states or resonances, scatter from the remaining third particle. We treat this effective two body problem by the partial wave matrix $\text{N}\text{D}$ method. We study in particular a coupled two channel problem, one channel consisting of one resonance plus one particle, the other of one bound state plus one particle. Our main purpose is to investigate in a full coupled channel situation the possible generation of three particle resonances. With single particle exchange forces forming the dynamical input to the $\text{N}\text{D}$ integral equations, enhancements are generated in a spinless model which correspond to three-particle resonances. The model is then applied, with spin included, to the $\text{p + p +}{}^{12}\text{C}$ system at low energy, in which ($\text{p +}{}^{12}\text{C}$) can form either the bound state ¹³N (G.S.) or the resonance ¹³N¹ (1.944 Mev); the two channels are then $\text{p +}{}^{13}\text{N(G.S.)}$ and $\text{p +}{}^{13}\text{N}{}^1$. The p-p interaction is neglected. It is found that the main effect in this case is the force arising from the coupling of the channels, which is sufficiently strong to generate a three particle level in the composite system ¹⁴O.