Di-trinucleon resonance states ofA=6systems in a microscopic cluster model

Abstract

Highly excited resonance states lying above the $t+t$ threshold in $^{6}\mathrm{He}$ are theoretically studied by the $t+t$ microscopic two-cluster model. The $t+t$ two-body scattering problem is solved by the microscopic $R$-matrix method in order to localize resonance states. Excited states of $^{6}\mathrm{Be}$ and $^{6}\mathrm{Li}$ (both $T=1$ and 0) are as well studied within the consistent two-cluster models. We have employed four different effective nucleon-nucleon interactions in order to check the sensitivity to our results and we have obtained fairly consistent results in every interaction. In positive parity states, our model gives deeply bound states which are well-known low-lying $\ensuremath{\alpha}+n+n$ three-body states and these states are obtained through the overlap between the $t+t$ and $\ensuremath{\alpha}+n+n$ configurations at smaller cluster relative distance. Similar bound states are found in the $T=0$ state in $^{6}\mathrm{Li}$. In negative parity states, our calculation shows broad ${0}^{\ensuremath{-}}$ and ${2}^{\ensuremath{-}}$ $P$-wave resonances just above the $t+t$ threshold and in addition three $F$-wave resonances of ${2}^{\ensuremath{-}}$, ${3}^{\ensuremath{-}}$, and ${4}^{\ensuremath{-}}$ at higher energies with broader widths. Our calculations show that the noncentral term of the effective nucleon-nucleon interaction plays an important role for these broad resonance states. $T=0$ states of $^{6}\mathrm{Li}$ show single broad resonances in $P$- and $F$-waves, respectively, and their positions are very close to those of $T=1$ resonances.