Electromagnetic transitions inC13andN13

The absolute and relative $\gamma$-decay strengths of the lowest $T=\frac{3}{2}$ levels in ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ are compared using the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(p,{\gamma }_0){}_{}{}^{13}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}({}_{}{}^3{}_{}{}^{}\mathrm{He},p\gamma ){}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, and ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}({}_{}{}^3{}_{}{}^{}\mathrm{He},n\gamma ){}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ reactions. By combining the present results with previous measurements, reduced asymmetries of $\frac{B\left({}_{}{}^{13}{}_{}{}^{}\mathrm{C}\right)}{B\left({}_{}{}^{13}{}_{}{}^{}\mathrm{N}\right)}-1=-0.07\mathrm{}\pm 0.13$, ${0.82}_{-0.6\mathrm{}}^{+1.2\mathrm{}}$, ≤0.83 ± 0.29, and -0.04 ± 0.14 are obtained for the ${\gamma }_0\mathrm{}\left(M1\mathrm{}\right)\mathrm{}$, ${\gamma }_0\mathrm{}\left(E2\mathrm{}\right)\mathrm{}$, ${\gamma }_1\mathrm{}\left(E1\mathrm{}\right)\mathrm{}$, and ${\gamma }_2\mathrm{}\left(M1\mathrm{}\right)\mathrm{}$ transitions, respectively. All of the known mirror $\gamma$ transitions in mass 13 are summarized and compared with theoretical calculations and with the analogous $\beta$ decays of ${}_{}{}^{13}{}_{}{}^{}\mathrm{B}$ and ${}_{}{}^{13}{}_{}{}^{}\mathrm{O}$. Upper limits of 2-7% are placed on the relative size of the isotensor transition matrix elements for the $M1\mathrm{}$ transitions. Changes in the radial wave functions induced by binding energy differences in ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ do not account for the observed asymmetry of the well known $E1\mathrm{}$ decays of the first excited states. This provides clear evidence of charge dependent parentage differences in the $T$-allowed components of the nuclear wave functions. For the lowest $T=\frac{3}{2}$ levels in ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ we find $\frac{{\Gamma }_{\gamma 0}}{\Gamma \left({}_{}{}^{13}{}_{}{}^{}\mathrm{C}\right)}=(0.396\mathrm{}\pm 0.030)\%$, $\frac{{\Gamma }_{\gamma 0}}{{\Gamma }_{p0\mathrm{}}\left({}_{}{}^{13}{}_{}{}^{}\mathrm{N}\right)}=(12.1\mathrm{}\pm 1.1)\%$, $\frac{{\Gamma }_{p0\mathrm{}}{\Gamma }_{\gamma 0}}{\Gamma \left({}_{}{}^{13}{}_{}{}^{}\mathrm{N}\right)}=(5.79\mathrm{}\pm 0.20)$ eV, ${\Gamma }_{\mathrm{total}}\left({}_{}{}^{13}{}_{}{}^{}\mathrm{C}\right)=(5.88\mathrm{}\pm 0.81)$ keV, and ${\Gamma }_{\mathrm{total}}\left({}_{}{}^{13}{}_{}{}^{}\mathrm{N}\right)=(0.86\mathrm{}\pm 0.12)$ keV. A new efficiency calibration standard at $E_{\gamma }=15.1\mathrm{}$ MeV is provided by our measurement of the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(p,{\gamma }_0){}_{}{}^{13}{}_{}{}^{}\mathrm{N}$ thick-target resonant yield, $Y_R=(6.83\mathrm{}\pm 0.22)\times {10}^{-9\mathrm{}} {\gamma }_0$'s per incident proton.