Emergence of the nuclear halo in ${}^{22}$C: Bridging shape and shell

The structure of ${}^{22}$C remains unsettled more than a decade after the 2010 reaction-cross-section measurement. The nucleus sits at $N=16$, where the spherical closure of ${}^{24}$O competes with the deformation of ${}^{20}$C. We develop a multi-reference density functional approach that restores particle number and angular momentum and mixes quadrupole shapes while retaining the continuum. The calculation gives a deformed two-neutron halo with matter radius of 3.29 fm, closer to the carbon-target extraction, and a long $s$-wave tail. The ground state $0_1^{+}$ is dominated by oblate configurations, with $B(E2)$ values comparable to those of ${}^{20}$C. The valence neutrons occupy mixed $sd$ orbits; the $N=16$ closure established in ${}^{24}$O is substantially weakened in ${}^{22}$C.