Final-state interactions and spin structure in E1 breakup of Li11 in halo effective field theory

Abstract

We calculate the $E1$ breakup of the $2n$ halo nucleus $^{11}\mathrm{Li}$ in halo effective field theory (Halo EFT) at leading order. In Halo EFT, $^{11}\mathrm{Li}$ is treated as a three-body system of a $^{9}\mathrm{Li}$ core and two neutrons. We present a detailed investigation of final-state interactions (FSIs) in the neutron-neutron $(nn)$ and neutron-core $(nc)$ channels. We employ M\o{}ller 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-$^{9}\mathrm{Li}$ 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 $^{9}\mathrm{Li}$ is neglected.