Gamow-Teller sum rules and theC14(Li6,He6)N14reaction

A correlation between the (${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^6{}_{}{}^{}\mathrm{He}$) cross sections and the Gamow-Teller strength observed previously for other targets persists in the ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$(${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^6{}_{}{}^{}\mathrm{He}$)${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ reaction. The total Gamow-Teller strength up to 12 MeV excitation is measured and we derive sum rules for the Gamow-Teller strength which depend on the $\mathrm{LS}$ configurations of the target state. The extracted $\mathrm{LS}$ configuration of the ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ ground state is in serious disagreement with shell model calculations. There are several inconsistencies within our understanding of the nuclear structure and transition strengths in these nuclei, part of which is attributable to mesonic currents. Constraints are also placed upon the (${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^6{}_{}{}^{}\mathrm{He}$) reaction mechanism.