The cross sections and angular correlations for neutron emission to various states in the residual nucleus, following the ${}^{13}\mathrm{C}{(e,e}^{\prime }n)$ reaction, have been measured over the excitation energy range 8–27 MeV at the effective momentum transfer of 0.35 ${\mathrm{fm}}^{\mathrm{-}1}$. In the pygmy resonance, neutron emission leads predominantly to the ground and first excited states of ${}^{12}\mathrm{C},$ while in the giant resonance it leads to population of two higher excited states (12.71 MeV, $T=0;$ 15.11 MeV, $T=1).\mathrm{}$ This is the first direct observation for neutron population of these states. The isospin assignments of the resonances are made as a result of the observed decays. The branching ratio of the transition to the $T=1\mathrm{}$ states compared to the total cross section for neutron emission is found to be $19\pm 5\%,$ which is inconsistent with the theoretical predictions of about 50%. Both isospin splitting and the relative $T_{<}$ and $T_{>}$ strengths of the giant resonance are obtained for the neutron decay. The angular-correlation parameters for the decay of the giant dipole resonance are very similar for ${}^{13}\mathrm{C}$ and ${}^{12}\mathrm{C},$ which provides some support for a weak coupling model in which the giant resonance for ${}^{13}\mathrm{C}$ proceeds via core excitations in ${}^{12}\mathrm{C}.$

• Received 24 November 1997

DOI:https://doi.org/10.1103/PhysRevC.60.034309