Title:

RMatrix and Dynamical Theory of ThreeBody Resonances

Rmatrix theory is applied to threebody resonances by treating the decay as two sequential
twobody 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
twoneutron emission.
In this work threebody Rmatrix theory is ~pplied to the 1.8 MeV 2+ resonance in
6He, as the interactions of the twobody 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 . a + n +n
(ii) 6He(2+) ~ 2n(O+) + a ~ a + 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 Rmatrix decay routes interfere
coherently or incoherently, fully dynamical threebody hyperspherical harmonic (HH)
calculations are also performed. The HH calculations produce a single value for the total
width of the threebody 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 twoproton decay found in the literature.
