Charge and matter form factors of two-neutron halo nuclei in halo effective field theory at next-to-leading order

By using halo effective field theory (EFT), an expansion in ${R}_{\text{core}}/{R}_{\text{halo}}$, where ${R}_{\text{core}}$ is the radius of the core and ${R}_{\text{halo}}$ the radius of the halo nucleus, the charge and neutron form factors of the two-neutron halo nuclei $^{11}\mathrm{Li}, ^{14}\mathrm{Be}$, and $^{22}\mathrm{C}$ are calculated to next-to-leading order (NLO) by treating them as an effective three-body system. From the form factors, the point-charge and point-matter radii, inter-neutron distances, and neutron opening angles are extracted. Agreement is found with existing experimental extractions. Results are given for the point-charge and point-matter radii for arbitrary neutron core scattering effective range ${\ensuremath{\rho}}_{cn}$, which can be used for predictions once ${\ensuremath{\rho}}_{cn}$ is measured. Estimates for ${\ensuremath{\rho}}_{cn}$ are also used to make NLO predictions. Finally, the point-charge radii of this work are compared with other halo-EFT predictions, and setting the core mass equal to the neutron mass the point-charge radius is found to agree with an analytical prediction in the unitary limit.