Unified weak-coupling model of mass 13 nuclei, including exchange effects

Structure calculations on ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ are reported which use the weak-coupling model as a starting point. The same model is used for both positive- and negative-parity states. Exchange effects, which are especially important in the negative-parity states, are included by perturbation theory. ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ core states used are $0^{+}$, $2^{+}$, $0^{+*}$, $3^{-}$, $4^{+}$, and single-particle shell model states up through the $s-d$ shell (plus the $1f_{\frac{7}{2}}$, in one case) are included. Energy levels, moments, and transition rates are calculated and compared, where possible, with experiment. Generally, the results are excellent, except for $E1\mathrm{}$ rates. Effective charges are used in the electromagnetic rate results.