Gamma Decays of the FirstT=32States inBe9andB9

The reactions ${}_{}{}^7{}_{}{}^{}\mathrm{Li}({}_{}{}^3{}_{}{}^{}\mathrm{He},p){}_{}{}^9{}_{}{}^{}\mathrm{Be}\left(14.39\mathrm{} \mathrm{MeV}\right)\left(\gamma \right)$ and ${}_{}{}^7{}_{}{}^{}\mathrm{Li}({}_{}{}^3{}_{}{}^{}\mathrm{He},n){}_{}{}^9{}_{}{}^{}\mathrm{B}\left(14.67\mathrm{} \mathrm{MeV}\right)\left(\gamma \right)$ have been used to study the $\gamma$-decay modes of the first $T=\frac{3}{2}$ states in ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ and ${}_{}{}^9{}_{}{}^{}\mathrm{B}$. $\gamma$ spectra from a NaI detector were recorded in coincidence with proton energy spectra from the ${}_{}{}^7{}_{}{}^{}\mathrm{Li}({}_{}{}^3{}_{}{}^{}\mathrm{He},p)$ reaction, and with neutron time-of-flight spectra from the ${}_{}{}^7{}_{}{}^{}\mathrm{Li}({}_{}{}^3{}_{}{}^{}\mathrm{He},n)$ reaction. In addition, the singles $\gamma$ spectrum from the 14.39-MeV state in ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ was studied using a Ge-Li detector. The $\gamma$ spectrum from the Ge-Li detector gives the branching ratio $\frac{{\Gamma }_{\gamma \mathrm{}\left(2.43\right)\mathrm{}}}{{\Gamma }_{\gamma 0}}=1.19\mathrm{}\pm 0.16$ for the decay of the first $T=\frac{3}{2}$ state in ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$. From the $\gamma -n$ coincidence spectrum below threshold for production of ${}_{}{}^9{}_{}{}^{}\mathrm{B}$(14.67 MeV) a $\gamma$ decay from ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$(14.39 MeV) to a state in ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ at $E_x=2.9\mathrm{}\pm 0.25$ MeV was found. The total width of this state was found to be $\Gamma =1.0\mathrm{}\pm 0.25$ MeV. A measurement of the strength of this $\gamma$ branch relative to that to ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$(2.43 MeV) yields $\frac{{\Gamma }_{\gamma \mathrm{}\left(2.9\right)\mathrm{}}}{{\Gamma }_{\gamma \mathrm{}\left(2.43\right)\mathrm{}}}=0.30\mathrm{}\pm 0.04$. From the $\gamma -n$ spectra above the ${}_{}{}^9{}_{}{}^{}\mathrm{B}$(14.67 MeV) threshold a $\gamma$-decay spectrum from the (14.67-MeV) state in ${}_{}{}^9{}_{}{}^{}\mathrm{B}$ was obtained which shows consistency with the branching ratios obtained for ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$(14.39 MeV). Combining our branching ratios with previously available information allows us to present a best set of radiative widths from the first $T=\frac{3}{2}$ levels in ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ and ${}_{}{}^9{}_{}{}^{}\mathrm{B}$. From the coincidence spectra the value for $\frac{{\Gamma }_{\gamma 0}}{{\Gamma }_{\mathrm{tot}}}$ is found to be 0.021±0.004 for ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$(14.39 MeV). The ratios of the total widths $\frac{{\Gamma }_{\mathrm{tot}}\left({}_{}{}^9{}_{}{}^{}\mathrm{Be}\right(14.39\mathrm{} \mathrm{MeV}\left)\right)}{{\Gamma }_{\mathrm{tot}}\left({}_{}{}^9{}_{}{}^{}\mathrm{B}\right(14.67\mathrm{} \mathrm{MeV}\left)\right)}$ is deduced as ${1.23}_{-0.43\mathrm{}}^{+0.54\mathrm{}}$. When combined with the value for ${\Gamma }_0\left({}_{}{}^9{}_{}{}^{}\mathrm{Be}\right(14.39\mathrm{} \mathrm{MeV}\left)\right)$, these ratios yield ${\Gamma }_{\mathrm{tot}}=0.50\mathrm{}\pm 0.1$ keV (${}_{}{}^9{}_{}{}^{}\mathrm{Be}$) and ${0.4}_{-0.18\mathrm{}}^{+0.14\mathrm{}}$ keV (${}_{}{}^9{}_{}{}^{}\mathrm{B}$) for the total widths of the two states.