Three-body decays and R-matrix analyses

The R-matrix simulation of three-body decays is investigated as function of available Q value and the energy and width of the intermediate two-body resonance. We use three alpha-decaying unnatural parity states of C-12 for illustration. The energy distributions are shown to be sensitive to the parameters when the two-body energy is significantly smaller than Q and the width is smaller than about 0.5 MeV. The sequential decay inherent in the R-matrix formalism can then be distinguished from direct decay. We provide conditions for the validity of R-matrix analyses. We compare with full three-body computations of the same energy distributions where we also attempt to distinguish between sequential and direct decays. The results give a good reproduction of available experimental data and are consistent with the conclusions from R-matrix analyses. Nodes in the momentum distributions arise from angular momentum and parity conservation. Combined with symmetry requirements this constrains the momentum distributions significantly in some cases. Effects of interactions and decay mechanisms can only be seen in the remaining behavior as, e.g., additional nodes related to nodes in the coordinate wave function at large distance.