The nuclear magic numbers, as we know in stable nuclei, consist of two different series of numbers. The first series -- 2, 8, 20 -- is attributed to the harmonic oscillator potential, while the second one -- 28, 50, 82, and 126 -- is due to the spin-orbit (SO) interactions. The spin-orbit interactions are known to be significant and responsible for the large (spin-orbit) splitting of the single-particle states in heavy nuclei. These splittings, however, are expected to diminish in light nuclei due to low orbital angular momenta. This general expectation is supported by the fact that there is an apparent lack of fingerprints for a `magic number' (subshell closure) at 6 or 14 , which might have arisen from the widening 1p1/2-1p3/2 and 1d3/2-1d5/2 gaps, respectively, in the stable nuclei. A possible subshell closure at N=6 has been suggested both theoretically  and experimentally  in the very neutron-rich 8He isotope. For Z=6 and 14, possible subshell closures have been suggested  in the semi-magic 14C and 34Si.
In this talk, we will present experimental evidence for a prevalent subshell closure at proton number Z=6 in the neutron-rich carbon isotopes. We investigated (i) the point proton density distribution radii, combining our recent data for Be, B and C isotopes measured at RCNP, Osaka University and GSI, Darmstadt, with the available data from Ref. ; (ii) the atomic masses ; and (iii) the electromagnetic transition strengths  for a wide range of isotopes. Our systematic analysis revealed marked regularities which support a prominent proton `magic number' Z=6 in 13-20C.
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