Electromagnetic transitions in /sup 13/C and /sup 13/N

The absolute and relative $\ensuremath{\gamma}$-decay strengths of the lowest $T=\frac{3}{2}$ levels in $^{13}\mathrm{C}$ and $^{13}\mathrm{N}$ are compared using the $^{12}\mathrm{C}(p,{\ensuremath{\gamma}}_{0})^{13}\mathrm{N}$, $^{11}\mathrm{B}(^{3}\mathrm{He},p\ensuremath{\gamma})^{13}\mathrm{C}$, and $^{11}\mathrm{B}(^{3}\mathrm{He},n\ensuremath{\gamma})^{13}\mathrm{N}$ reactions. By combining the present results with previous measurements, reduced asymmetries of $\frac{B(^{13}\mathrm{C})}{B(^{13}\mathrm{N})}\ensuremath{-}1=\ensuremath{-}0.07\ifmmode\pm\else\textpm\fi{}0.13$, ${0.82}_{\ensuremath{-}0.6}^{+1.2}$, \ensuremath{\le}0.83 \ifmmode\pm\else\textpm\fi{} 0.29, and -0.04 \ifmmode\pm\else\textpm\fi{} 0.14 are obtained for the ${\ensuremath{\gamma}}_{0}(M1)$, ${\ensuremath{\gamma}}_{0}(E2)$, ${\ensuremath{\gamma}}_{1}(E1)$, and ${\ensuremath{\gamma}}_{2}(M1)$ transitions, respectively. All of the known mirror $\ensuremath{\gamma}$ transitions in mass 13 are summarized and compared with theoretical calculations and with the analogous $\ensuremath{\beta}$ 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 $M1$ 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 $E1$ 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 $\frac{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}0}}{\ensuremath{\Gamma}(^{13}\mathrm{C})}=(0.396\ifmmode\pm\else\textpm\fi{}0.030)%$, $\frac{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}0}}{{\ensuremath{\Gamma}}_{p0}(^{13}\mathrm{N})}=(12.1\ifmmode\pm\else\textpm\fi{}1.1)%$, $\frac{{\ensuremath{\Gamma}}_{p0}{\ensuremath{\Gamma}}_{\ensuremath{\gamma}0}}{\ensuremath{\Gamma}(^{13}\mathrm{N})}=(5.79\ifmmode\pm\else\textpm\fi{}0.20)$ eV, ${\ensuremath{\Gamma}}_{\mathrm{total}}(^{13}\mathrm{C})=(5.88\ifmmode\pm\else\textpm\fi{}0.81)$ keV, and ${\ensuremath{\Gamma}}_{\mathrm{total}}(^{13}\mathrm{N})=(0.86\ifmmode\pm\else\textpm\fi{}0.12)$ keV. A new efficiency calibration standard at ${E}_{\ensuremath{\gamma}}=15.1$ MeV is provided by our measurement of the $^{12}\mathrm{C}(p,{\ensuremath{\gamma}}_{0})^{13}\mathrm{N}$ thick-target resonant yield, ${Y}_{R}=(6.83\ifmmode\pm\else\textpm\fi{}0.22)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9} {\ensuremath{\gamma}}_{0}$'s per incident proton.[NUCLEAR REACTIONS $^{12}\mathrm{C}(p,{\ensuremath{\gamma}}_{0})$, $E=14.23$ MeV resonance; $^{11}\mathrm{B}(^{3}\mathrm{He},p\ensuremath{\gamma})$, $^{11}\mathrm{B}(^{3}\mathrm{He},n\ensuremath{\gamma})$, particle-$\ensuremath{\gamma}$ coincidence; measured $\frac{{\ensuremath{\Gamma}}_{\ensuremath{\gamma}i}}{\ensuremath{\Gamma}}$ and deduced ${\ensuremath{\Gamma}}_{{\ensuremath{\gamma}}_{i}}$ and $\ensuremath{\Gamma}$ for $^{13}\mathrm{C}$ ($T=\frac{3}{2}$) and $^{13}\mathrm{N}$ ($T=\frac{3}{2}$); symmetry of mirror transitions.]