Uncertainty quantified three-body model applied to the two-neutron halo $^{22}$C

Two-neutron halo nuclei offer a fascinating probe into the behaviour of quantum few-body systems at the limits of binding. Although few nuclei have already been clearly identified, many of their properties remain poorly constrained. $^{22}$C, one of the heaviest, still lacks a precise identification of its static and dynamic properties, such as its mass and dipole strength in the continuum. One main difficulty is that properties of two-neutron halo nuclei are inferred from experimental data using a theoretical model. Therefore, accurately determining the characteristics of two-neutron halo nuclei requires an accurate theoretical model and careful quantification of the uncertainties. In this work, we examine $^{22}$C with a three-body model, seeing $^{22}$C as a $^{20}$C core and two halo neutrons, and quantify for the first time the uncertainties associated with the $^{20}$C-$n$ interaction using a Bayesian approach. We propagate these uncertainties to properties of bound and scattering states of $^{22}$C, as well as its dipole strength. The comparison of our prediction for the matter radius to experimentally-derived values suggests that $^{22}$C is bound by less than 0.35~MeV and is dominated by a $(s_{1/2})^2$ configuration. Our analysis of the dipole strength shows that final-state interaction needs to be included for an accurate description, the uncertainties on the strength function are about 50\% and are mostly influenced by uncertainties on the ground-state properties, and partial-wave occupation of $^{22}$C depends on the scattering length and the $d_{3/2}$ resonance energy of the $^{20}$C-$n$ unbound system. Such sensitivity of the dipole strength to the properties of both $^{21}$C and $^{22}$C properties motivates a precise measurement of the $^{22}$C dipole strength function, that will allow to precisely and accurately resolve the spectroscopy of these nuclei.