Mirror states inA=15from 60-MeVLi6-induced reactions onC12

Analog pairs of states have been observed simultaneously with counter telescopes by using the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^6{}_{}{}^{}\mathrm{Li}, t)$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$) reactions for $E\left({}_{}{}^6{}_{}{}^{}\mathrm{Li}\right)=60\mathrm{}$ MeV at excitation energies of 10.45-10.73, 12.84-13.15, and 15.05-15.49 MeV in ${}_{}{}^{15}{}_{}{}^{}\mathrm{O}$-${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$, respectively. Magnetic spectrograph data for the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^6{}_{}{}^{}\mathrm{Li}, t){}_{}{}^{15}{}_{}{}^{}\mathrm{O}$ reaction having an energy resolution of 50 keV versus the 200 keV resolution of the counter systems show that single states are being strongly excited at 10.45, 12.84, and 15.05 MeV in ${}_{}{}^{15}{}_{}{}^{}\mathrm{O}$. Elastic and inelastic scattering data have also been taken in the angular range from 10 to 120° c.m. with $\Delta \theta \approx 2°$. Optical model parameters were extracted from the elastic scattering data, and quadrupole deformation lengths were obtained from a coupled-channels analysis of the inelastic scattering data to the $2^{+}$, 4.43-MeV state in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. Exact finite-range distorted-wave Born-approximation calculations for the transfer reactions yield a range of $L$ transfers for each of the analog states which are consistent with the assumption that these states have spins $J_f\ge \frac{9}{2}$.