Final-state interactions and spin structure in \(E1\) breakup of \(^11\)Li in Halo EFT

We calculate the \(E1\) breakup of the \(2n\) halo nucleus \(^{11}\)Li in Halo Effective Field Theory (Halo EFT) at leading order. In Halo EFT, \(^{11}\)Li is treated as a three-body system of a \(^{9}\)Li core and two neutrons. We present a detailed investigation of final-state interactions (FSI) in the neutron-neutron \((nn)\) and neutron-core \((nc)\) channels. We employ Moller operators to formulate an expansion scheme that satisfies the non-energy-weighted cluster sum rule and successively includes higher-order terms in the multiple-scattering series for the FSI. Computing the \(E1\) strength up to third order in this scheme, we observe apparent convergence and good agreement with experiment. The neutron-neutron FSI is by far the most important contribution and largely determines the maximum value of the \(E1\) distribution. However, inclusion of \(nc\) FSI does shift the peak position to slightly lower energies. Moreover, we investigate the sensitivity of the \(E1\) response to the spin structure of the neutron-\({}^9\)Li interaction. We contrast results for an interaction that is the same in the spin-1 and spin-2 channels with one that is only operative in the spin-2 channel, and find that good agreement with experimental data is only obtained if the interaction is present in both spin channels. The latter case is shown to be equivalent to a calculation in which the spin of \(^9\)Li is neglected.