E2andM1Matrix Elements inB10

$\gamma$-ray decay of the ${\mathrm{B}}^{10}$ 2.15- and 3.59-MeV levels was studied following population via the ${\mathrm{B}}^{11}({\mathrm{He}}^3, \alpha ){\mathrm{B}}^{10}$ reaction at $E_{{\mathrm{He}}^3}=2.6\mathrm{}$ MeV. The $\gamma$ rays were detected in coincidence with $\alpha$ particles observed in an axially symmetric silicon detector centered at 180° to the beam. $\gamma$-ray branching ratios were extracted for both levels. From the angular distributions of the decay $\gamma$ rays, results were obtained for the $\frac{E2\mathrm{}}{M1\mathrm{}}$ mixing ratios $x$ of the decay of the $2^{+}$ 3.59-MeV level to the $3^{+}$ ground state, the $1^{+}$ 0.72-MeV level, and the $1^{+}$ 2.15-MeV level, respectively, as follows: $+0.31<x<+2.1\mathrm{}$, $x^{-1\mathrm{}}=+(0.11\mathrm{}\pm 0.10)$, $x=-(0.38\mathrm{}\pm 0.09)$, all pertaining to $\Delta T=0\mathrm{}$ transitions. For the decay of the 2.15-MeV level to the 0.72-MeV level, $x=-(0.29\mathrm{}\pm 0.05) or -(3.39\mathrm{}\pm 0.55)$. Combining these results with previous work gives information on the magnitudes as well as the relative phases of the $M1\mathrm{}$ and $E2\mathrm{}$ matrix elements considered. These results are compared with the predictions of the independent-particle model.