The ${}^{10}$Li spectrum and the ${}^{11}$Li properties

Abstract

The neutron--${}^9$Li interaction and the corresponding low-energy ${}^{10}$Li spectrum are decisive for the properties of ${}^{11}$Li described as a three-body system (n+n+${}^9$Li). We compute structure and breakup properties of ${}^{11}$Li as function of this interaction. The hyperfine structure due to the spin 3/2 of both ${}^9$Li and ${}^{11}$Li is needed and treated with special care. We use the hyperspherical adiabatic expansion of the Faddeev equations for the structure and the participant-spectator model for the breakup reactions of ${}^{11}$Li. We use established experimental constraints of both ${}^{11}$Li (binding energy, size and differential breakup cross sections) and of ${}^{10}$Li (a virtual s-state below 50 keV and a $p$-resonance around 0.54 MeV).Another $p$-resonance must then be present below 0.54 MeV and another $s$-level must be present between about 0.5 MeV and 1 MeV depending on unknown spin assignments. All established facts are in agreement with our predictions obtained within the same consistent model.

Comments: 27 pages, 8 figures