Four-body extension of the continuum-discretized coupled-channels method

Abstract

I develop an extension of the continuum-discretized coupled-channels (CDCC) method to reactions where both nuclei present a low breakup threshold. This leads to a four-body model, where the only inputs are the interactions describing the colliding nuclei, and the four optical potentials between the fragments. Once these potentials are chosen, the model does not contain any additional parameter. First I briefly discuss the general formalism, and emphasize the need for dealing with large coupled-channel systems. The method is tested with existing benchmarks on $4\ensuremath{\alpha}$ bound states with the Ali-Bodmer potential. Then I apply the four-body CDCC to the $^{11}\mathrm{Be}+d$ system, where I consider the $^{10}\mathrm{Be}({0}^{+},{2}^{+})+n$ configuration for $^{11}\mathrm{Be}$. I show that breakup channels are crucial to reproduce the elastic cross section, but that core excitation plays a weak role. The $^{7}\mathrm{Li}+d$ system is investigated with an $\ensuremath{\alpha}+t$ cluster model for $^{7}\mathrm{Li}$. I show that breakup channels significantly improve the agreement with the experimental cross section, but an additional imaginary term, simulating missing transfer channels, is necessary. The full CDCC results can be interpreted by equivalent potentials. For both systems, the real part is weakly affected by breakup channels, but the imaginary part is strongly modified. I suggest that the present wave functions could be used in future DWBA calculations.