Isospin mixing in the ${}_{}{}^2{}_{}{}^{}\mathrm{H}(\alpha ,\alpha p)n$ reaction

We calculate the ${}_{}{}^2{}_{}{}^{}\mathrm{H}(\alpha ,\alpha ){}_{}{}^2{}_{}{}^{}\mathrm{H}_{}^{*}{}_{}{}^{}$ isospin forbidden transition in a nucleon-alpha impulse approximation which includes higher order terms. The results agree qualitatively with the interpretations of experiments which favor a departure from isospin conservation of a few percent at $E_{\alpha }\simeq 24$ MeV and of the order of 30% at $E_{\alpha }\simeq 13$ MeV. The interplay of Coulomb and spin-orbit effects causing the transition to the singlet deuteron is elucidated and the energy and angular dependence of the $d^{*}$ production is presented. A comparison is made with the intermediate coupling shell model of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ and isospin mixing in the $2^{+}$(4.31, $T=0\mathrm{}$) and $2^{+}$ (5.36, $T=1\mathrm{}$) states is calculated to be of the order of 0.5%. This suggests that the production of the $d^{*}$ occurs through a direct reaction.

[NUCLEAR REACTIONS Deuteron breakup by alphas, theoretical prediction of singlet deuteron production in ${}_{}{}^2{}_{}{}^{}\mathrm{H}(\alpha ,\alpha p)n$; isospin violation explained by differences in $n$ alpha and $p$ alpha on shell $T$ matrices.]