Properties of Lithium-11 and Carbon-22 at leading order in halo effective field theory

We study the ¹¹Li and ²²C nuclei at leading order (LO) in halo effective field theory (Halo EFT). Using the value of the ²²C rms matter radius deduced in Ref. [1] as an input in a LO calculation, we simultaneously constrain the values of the two-neutron (2n) separation energy of ²²C and the virtual-state energy of the ²⁰C-neutron system (hereafter denoted ²¹C). The 1-σ uncertainty of the input rms matter radius datum, along with the theory error estimated from the anticipated size of the higher-order terms in the Halo EFT expansion, gives an upper bound of about 100 keV for the 2n separation energy. We also study the electric dipole excitation of 2n halo nuclei to a continuum state of two neutrons and the core at LO in Halo EFT. We first compare our results with the ¹¹Li data from a Coulomb dissociation experiment and obtain good agreement within the theoretical uncertainty of a LO calculation. We then obtain the low-energy spectrum of B(E1) of this transition at several different values of the 2n separation energy of ²²C and the virtual-state energy of ²¹C. Our predictions can be compared to the outcome of an ongoing experiment on the Coulomb dissociation of ²²C to obtain tighter constraints on the two- and three-body energies in the ²²C system.