Constraints on two-neutron separation energy in the Borromean $^{22}$C nucleus

TL;DR

This paper uses a three-body model to constrain the two-neutron separation energy in the Borromean nucleus $^{22}$C, suggesting it is below 0.4 MeV and exploring the potential for Efimov states.

Contribution

It provides new constraints on the two-neutron separation energy in $^{22}$C and proposes experimental energy regions for studying the unbound $^{21}$C state.

Findings

Two-neutron separation energy in $^{22}$C is below ~0.4 MeV.

$^{22}$C may host an excited Efimov state or a three-body resonance.

$^{21}$C virtual state energy is close to zero.

Abstract

The recently extracted matter radius of carbon isotope $^{22}$C allows us to estimate the mean-square distance of a halo neutron with respect to the center-of-mass of this nucleus. By considering this information, we suggest an energy region for an experimental investigation of the unbound $^{21}$C virtual state. Our analysis, in a renormalized zero-ranged three-body model, also indicates that the two-neutron separation energy in $^{22}$C is expected to be found below $\sim$0.4~MeV, where the $^{22}$C is approximated by a Borromean configuration with a pointlike $^{20}$C and two $s$-wave halo neutrons. A virtual-state energy of $^{21}$C close to zero, would make the $^{22}$C, within Borromean nuclei configurations, the most promising candidate to present an excited bound Efimov state or a continuum three-body resonance.