Emergent universality in the two-neutron halo structure of C22

Abstract

The structure of the two-neutron halo $^{22}\mathrm{C}$ is investigated by means of a renormalized zero-range three-body model, with interactions in the $s$-wave channel, and a finite-range model with two- and three-body forces provided by the hyperspherical adiabatic expansion method. In both models the halo wave function in configuration space is obtained by using as inputs the two-body scattering lengths and the two-neutron separation energy. The halo-matter density is computed for $^{22}\mathrm{C}$ with different three-body forces and low-energy parameters, with two-neutron separation energy within the range $50\phantom{\rule{4.pt}{0ex}}\text{keV}\ensuremath{\le}{S}_{2n}\ensuremath{\le}1000$ keV. The halo-neutron density depends weakly on the neutron-$^{20}\mathrm{C}$ scattering length as long as its absolute value is larger than the neutron-neutron one. The halo-neutron density is then analyzed by means of the root-mean-square radius, the probability density, and also the geometry, taking into account the angle between the two Jacobi coordinates. The results of finite-range and zero-range two-neutron-core models are compared. The effects in the halo structure of short-range and long-range three-body forces are studied, and the emergent universal behavior of the halo-neutron density and its geometry is pointed out.