Neutron skin and signature of the $N$ = 14 shell gap found from measured proton radii of ${}^{17-22}$N

A thick neutron skin emerges from the first determination of root mean square radii of the proton distributions for ${}^{17-22}$N from charge changing cross section measurements around 900$A$ MeV at GSI. Neutron halo effects are signaled for ${}^{22}$N from an increase in the proton and matter radii. The radii suggest an unconventional shell gap at $N$ = 14 arising from the attractive proton-neutron tensor interaction, in good agreement with shell model calculations. $Ab$ $initio$, in-medium similarity re-normalization group, calculations with a state-of-the-art chiral nucleon-nucleon and three-nucleon interaction reproduce well the data approaching the neutron drip-line isotopes but are challenged in explaining the complete isotopic trend of the radii.