Universality and the Coulomb dissociation of two-neutron halos

In the limit of large two-body s-wave scattering length few-body systems display {\it universality}: their properties are independent of the details of interactions. Such universality is present in halo nuclei where two neutrons orbit a tightly bound nuclear core. There, the neutron-neutron (nn) scattering length is much larger than the range of the nn force, and, if the neutron-core scattering length obeys $|a|\gg R$, the system can be described by an effective field theory (EFT) based on this separation of scales. In this ``Halo EFT" the degrees of freedom are the neutrons and the core; core structure is included at higher order in the EFT. At leading order (LO) in the $R/a$ expansion one three-body datum is needed as input to obtain renormalized predictions for core-n-n observables. Here we take that datum to be the two-neutron separation energy, $S_{2n}$, of a 2n-halo nucleus. At LO all properties of a 2n-halo are functions of $S_{2n}$ and the two-body scattering lengths. In particular, its Coulomb dissociation spectrum is a universal function of these parameters. We compute that function, and compare it to experimental data from $^{11}$Li. We also discuss how measurements of the Coulomb dissociation of $^{22}$C can constrain both its $S_{2n}$ and properties of $^{21}$C.