| Summary: | R-matrix theory is applied to three-body resonances by treating the decay as two sequential two-body decays. This allows the decay to proceed through up to three different decay routes, each with an associated width. From the literature it is unclear whether these widths should be combined incoherently or coherently, especially in the case of two-neutron emission. In this work three-body R-matrix theory is applied to the 1.8 MeV 2+ resonance in He, as the interactions of the two-body subsystems are well known. This resonance can decay via two possible routes, each going through an intermediate state; (i) 6He(2+) -5He(3/2- g.s.) + n → alpha + n + n (ii) 6He(2+) → 2n(0+) + alpha → alpha + n + n Limiting cases of the theory are explored, in particular the sensitivity to the shape of the probability density function (PDF) which describes the shape of the intermediate state. A new formula is developed for the PDF which allows for the choice of optimised boundary conditions. This is particularly important where the intermediate state is a virtual state. In order to determine whether the widths from the R-matrix decay routes interfere coherently or incoherently, fully dynamical three-body hyper spherical harmonic (HH) calculations are also performed. The HH calculations produce a single value for the total width of the three-body decay. It was found that the coherent and HH widths are in agreement, but both fall short of the experimentally measured value. This is consistent with the calculations for two-proton decay found in the literature.
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