Three-body structures of low-lying nuclear states of $^8$Li

The four nucleons in $^8$Li outside the $\alpha$-particle ($\alpha=^4$He) can be divided into pairs of one neutron ($n$) and 3 nucleons in the triton ($t=^3$H), or 2 in the deuteron ($d=^2$H) and two neutrons in a dineutron ($^2n$). The corresponding three-body structures, $\alpha$+$t$+$n$ or $\alpha$+$d$+$^2n$, are suggested to describe the bulk part of the low-energy ($<10$~MeV) states of $^8$Li. Several breakup thresholds influence the structures and possible decays. We calculate the three-body structures of the various $J^{\pi}$ states, where different clustering appear, e.g. $^7$Li*+$n$, $^6$Li*$+^2n$, $^6$He*$+d$. The experimental $^8$Li spectrum can be reproduced with fine tuning by a three-body potential parameter. Three unobserved $0^+$ and an excited 2$^+$ states are found. All states appear as bound states or resonances. The lowest or highest energies have cluster structures, $\alpha$+$t$+$n$ or $\alpha$+$d$+$^2n$, respectively. We give calculated energy and width (if possible), geometry, and partial wave decomposition for all states.