Neutron Pairing Correlations in an -- Three-Cluster Model of the He Nucleus

An -n-n three-cluster model of the He nucleus is studied by solving the Faddeev equations, where the cluster potential between and n takes into account the Pauli exclusion correction, using the Fish-Bone Optical Model (Schmid in Z Phys A 297:105, 1980). The resulting binding energy of the ground state () is 0.831 MeV and the resonance energy of the first excited state (), 0.60-i0.012 MeV, is extracted from the three-cluster break-up threshold. These theoretical values are in reasonable agreement with the experimental data: 0.973 MeV and 0.824-i0.056 MeV, respectively. In order to investigate the structure of these states, we calculate the angle density matrix for the angle in the triangle formed by the three clusters. The angle density matrix of the ground state has two peaks and the configuration of wave function corresponding to the peaks constitutes a mixture of an acute-angled triangle structure and an obtuse-angled one. This finding is consistent with the former result from a variational approach (Hagino and Sagawa in Phys Rev C 72:044321, 2005). On the other hand, in the case of state only a single peak is obtained.