Abstract
A correction term to the usual distorted-wave Born-approximation amplitude of the ($^{3}\mathrm{He},d$) reaction is derived by using Lane's t\ifmmode\cdot\else\textperiodcentered\fi{}T interaction. This interaction changes the $^{3}\mathrm{He}$ into $t$ and the target into its analog, and thus gives rise to a ($t,d$) reaction from this analog channel; the deuteron produced in this way is coherent with the deuteron produced by the straightforward ($^{3}\mathrm{He},d$) reaction. It is shown that this correaction term changes the value of the derived spectroscopic factor by an important amount, and makes it agree well, if not completely, with the value predicted by the shell-model calculation.
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