Isospin Selection Rule in theC12(d,α)B10Reaction

The violation of the isospin selection rule has been studied in the reaction ${\mathrm{C}}^{12}(d,\alpha ){\mathrm{B}}^{10}$ with deuteron energies between 9 and 12.5 MeV. The differential and total cross sections of the isospin-forbidden transition to the first $T=1\mathrm{}$ state in ${\mathrm{B}}^{10}$ (the $J^{\pi }=0^{+}$ state at 1.74-MeV excitation) have been compared with the cross sections of the isospin-allowed transitions to the ground state ($J^{\pi }=3^{+}$, $T=0\mathrm{}$), the first excited state ($J^{\pi }=1^{+}$, $T=0\mathrm{}$ at 0.72 MeV), and the third excited state ($J^{\pi }=1^{+}$, $T=0\mathrm{}$ at 2.14 MeV). Mostly the intensity of the $T=1\mathrm{}$ alpha group is less than 1% of the yield of the $\alpha$ groups leading to the neighboring $T=0\mathrm{}$ states. This reduction is due not only to isospin forbiddenness but also to angular-momentum and parity selection rules which apply in this particular ($d,\alpha$) reaction for which both the initial and the final state have $J^{\pi }=0^{+}$. These weighting factors have been calculated by use of the statistical theory of nuclear reactions. After these factors have been applied, the $T=1\mathrm{}$ alpha group has an intensity of about 10% relative to the other three $T=0\mathrm{}$ transitions at a deuteron energy of 9 MeV and 1-2% at an energy of 11 MeV. The small yield is ascribed to the isospin selection rules that to some extent govern this $T=1\mathrm{}$ transition. In the energy range from 9 to 11 MeV, the angular distribution of the $T=1\mathrm{}$ state stays fairly constant and is nearly symmetric around 90°. The yield decreases steadily. At deuteron energies higher than 11.5 MeV, the angular distribution changes drastically and becomes strongly forward peaked and asymmetric around 90°, and the total yield increases slightly. We assume that this behavior indicates a direct-interaction mechanism in which the process of mixing the isospins takes place at the surface of the nucleus. Coulomb excitation during the process of $d$ capture or $\alpha$ emission might be responsible for the isospin violation at these higher deuteron energies.