Nuclear charge radii of the carbon isotopes 12C, 13C and 14C

Muonic X-ray energies of the K-series of the carbon isotopes ¹³C and ¹⁴C have been determined relative to ¹²C. For the first time, muonic atom measurements using radioactive ¹⁴C have been performed. Model-independent equivalent nuclear charge radii R_k,α and their differences have been deduced. The R_k,α radii increase by 10(14) and 32(11) am respectively with the filling of the $\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ neutron Subshell. The results are compared with recent elastic electron scattering data. The former natural carbon data have been reanalysed using a new value for the nuclear polarization. In terms of the rms charge radius, we then obtain $\text{〈r}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 2.472(16)}\text{fm}$ for the ¹²C isotope.