Isospin forbidden ( alpha,d) transitions to the low-lying states in 26Al.

Abstract

The $^{24}\mathrm{Mg}$(\ensuremath{\alpha},d${)}^{26}$Al reaction leading to the 0.23 MeV ${0}_{1}^{+}$, T=1 and the 3.16 MeV ${2}_{2}^{+}$, T=1 states were measured at ${\mathit{E}}_{\mathrm{\ensuremath{\alpha}}}$=64.7 MeV. Cross sections for these isospin-forbidden transitions were compared with exact-finite-range second-order distorted wave Born approximation (DWBA) calculations for successive-transfer processes (\ensuremath{\alpha}${\mathrm{\ensuremath{-}}}^{3}$He-d) and (\ensuremath{\alpha}-t-d). The DWBA calculation with spectroscopic amplitudes obtained from the full sd-shell model was found to underestimate the cross section for the ${0}^{+}$ state by a factor of 200, while a normalization factor of 10 was obtained for the ${2}^{+}$ state. About 5% isospin impurity in the ${0}^{+}$ state of $^{26}\mathrm{Al}$ was required to obtain the same normalization for the ${0}^{+}$ state.