We carry out shell model calculations to study electromagnetic moments and electric dipole transitions of C isotopes. We point out the configuration dependence of the quadrupole and magnetic moments of the odd C isotopes, which will be useful to find out the deformations and the spin parities of the ground states of these nuclei. We also study the electric dipole states of C isotopes, focusing on the interplay between low energy pigmy strength and giant dipole resonances. As far as the energies of the resonances are concerned, reasonable agreement is obtained with available experimental data for the photoreaction cross sections in ${}^{12}\mathrm{C},$ ${}^{13}\mathrm{C},$ and ${}^{14}\mathrm{C},$ both in the low energy region below $ħ\omega =14\mathrm{}\mathrm{MeV}$ and in the high energy giant resonance region (14 MeV $<ħ\omega <~30\mathrm{MeV}).\mathrm{}$ The calculated transition strength below the giant dipole resonance $(ħ\omega <~14\mathrm{MeV})$ in C isotopes heavier than ${}^{15}\mathrm{C}$ is found to exhaust about $12–16\%$ of the classical Thomas-Reiche-Kuhn sum rule value and $50–80\%$ of the cluster sum rule value.

• Received 15 July 2002

DOI:https://doi.org/10.1103/PhysRevC.68.014317