${}_{}{}^{11}{}_{}{}^{}\mathrm{Li}$+p elastic scatterings in a four-body model with the eikonal approximation

Elastic differential cross sections of ${}_{}{}^{11}{}_{}{}^{}\mathrm{Li}$ on a proton target recently observed at ${\mathit{E}}_{\mathrm{lab}}$/A=62 MeV are analyzed in a ${(}^9$Li+n+n)-p four-body model to take the halo structure of ${}_{}{}^{11}{}_{}{}^{}\mathrm{Li}$ into consideration. The eikonal and adiabatic approximations are employed to derive the optical potential that includes the breakup effect of halo neutrons to continuum states. It is shown that both the breakup of ${}_{}{}^{11}{}_{}{}^{}\mathrm{Li}$ and the exchange force of the n-p interaction lead to the reduced cross sections that are in satisfactory agreement with experiment with no adjustable parameters.