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Using halo effective field theory (EFT), an expansion in $R_{core}/R_{halo}$,where $R_{core}$ is the radius of the core and $R_{halo}$ the radius of thehalo nucleus, we calculate the charge and neutron form factors of thetwo-neutron halo nuclei $^{11}$Li, $^{14}$Be, and $^{22}$C tonext-to-leading-order (NLO) by treating them as an effective three-body system.From the form factors we extract the point charge and point matter radii,inter-neutron distance, and neutron opening angle. Agreement is found withexisting experimental extractions. Results are given for the point charge andpoint matter radii for arbitrary neutron core scattering effective range,$\rho_{cn}$, that can be used for predictions once $\rho_{cn}$ is measured.Estimates for $\rho_{cn}$ are also used to make NLO predictions. Finally, ourpoint charge radii are compared to other halo-EFT predictions, and setting thecore mass equal to the neutron mass our point charge radius is found to agreewith an analytical prediction in the unitary limit.

Charge and Matter Form Factors of Two-Neutron Halo Nuclei in Halo Effective Field Theory at Next-to-leading-order