Theoretical analysis of resonance states in ${}^{4}H$, ${}^{4}He$ and ${}^{4}Li$ above three-cluster threshold

Abstract

The resonance states of ${}^{4}H$, ${}^{4}He$ and ${}^{4}Li$, embedded in the three-cluster $d+N+N$ continuum, are investigated within a three-cluster model. The model treats the Pauli principle exactly and incorporates the Faddeev components for proper description of the boundary conditions for the two- and three-body continua. The hyperspherical harmonics are used to distinguish and numerate channels of the three-cluster continuum. It is shown that the effective barrier, created by three-cluster configuration $d+N+N$, is strong enough to accommodate two resonance states.

20 page, 4 figures