Disappearance of the $N=14$ shell gap in the C isotopic chain

Expérience GANIL, Dispositif SISSI, détécteur SPEG; The structure of $^{17-20}_{6}$C nuclei was investigated by means of the in-beam $\gamma$-ray spectroscopy technique using fragmentation reactions of radioactive beams. Based on particle-$\gamma$ and particle-$\gamma\gamma$ coincidence data, level schemes are constructed for the neutron rich $^{17-20}$C nuclei. The systematics of the first excited 2$^{+}$ states in the Carbon isotopes is extended for the first time to $A$=20 showing that in contrast to the case of the oxygen isotopes, the $N$=14 subshell closure disappears. Experimental results are compared with shell-model calculations. Agreement between them is found only if a reduced neutron--neutron effective interaction is used. Implications of this reduced interaction in some properties of weakly bound neutron-rich Carbon are discussed.