The charge symmetric scattering systems ${}^{12}{\mathrm{C}+}^{13}\mathrm{N}$ and ${}^{12}{\mathrm{C}+}^{13}\mathrm{C}$ have been investigated by using the orthogonalized coupled-reaction-channel (OCRC) method with the basis functions of the elastic, inelastic, and transfer channels defined by the single-particle states, $1p$$\frac{1}{2}$, $2s$$\frac{1}{2}$, $1d$$\frac{5}{2}$, and $1d$$\frac{3}{2}$ of the valence nucleon in ${}^{13}\mathrm{N}$ or ${}^{13}\mathrm{C}.$ The data of the elastic scattering of ${}^{13}\mathrm{N}$ on ${}^{12}\mathrm{C}$ measured by Liénard et al. have been explained consistently with the data of the elastic and inelastic scattering of the ${}^{12}{\mathrm{C}+}^{13}\mathrm{C}$ system. The CRC effects on both of the above systems are very strong, although those on the ${}^{12}{\mathrm{C}+}^{13}\mathrm{N}$ system are fairly weaker than the ${}^{12}{\mathrm{C}+}^{13}\mathrm{C}$ system. The role of the highly excited single-particle states $1d$$\frac{3}{2}$ is particularly important in the formation of a specific CRC scheme, i.e., the formation of the covalent molecules due to the hybridization caused by the mixing of the different parity single-particle states. The fusion cross sections of the ${}^{12}{\mathrm{C}+}^{13}\mathrm{C}$ system at energies below the Coulomb barrier are strongly enhanced as a result of the strong CRC effects as compared with those of the ${}^{12}{\mathrm{C}+}^{12}\mathrm{C}$ system, while in ${}^{12}{\mathrm{C}+}^{13}\mathrm{N}$ system the enhancement of the sub-barrier fusion has not been observed. The above absorption mechanism for the ${}^{12}{\mathrm{C}+}^{13}\mathrm{C}$ system explains the lack of the molecular-resonance phenomena observed in the ${}^{12}{\mathrm{C}+}^{12}\mathrm{C}$ system. We check the effects of the dipole $\mathrm{}\left(E1\mathrm{}\right)\mathrm{}$ transition of the valence nucleon in ${}^{13}\mathrm{N}$ (and also in ${}^{13}\mathrm{C}$) due to the core-core Coulomb interaction in the scattering at sub-barrier energies. The effects are not appreciable.

• Received 17 October 1996

DOI:https://doi.org/10.1103/PhysRevC.55.1946