Endothermic Deuteron Stripping Reactions. I. Stripping Near Threshold

Wilkinson's explanation of the good agreement between theory and experiment for low energy, low $Q$ value, ($d, p$) and ($d, n$) stripping reactions is restated from the point of view of the dispersion relations derivation of the Butler stripping formula. From this point of view, the kinematical conditions which should lead to the least distortion of the stripping pattern appear in a simple way. As a consequence of Wilkinson's arguments, it is proposed that the stripping mechanism should contribute significantly to endothermic ($d, p$) or ($d, n$) reactions near threshold. Some ($d, n$) threshold work is discussed, and it is concluded that this work gives some evidence that the stripping mechanism is important near threshold. The information on the reaction mechanism near threshold which can be obtained from $\gamma$-ray angular distribution measurements in ($d, p\gamma$) or ($d, n\gamma$) reactions is discussed and a general form for the angular distribution function for either plane-wave or distorted-wave stripping is developed. The ${\mathrm{B}}^{11}(d, n){\mathrm{C}}^{12}$ (15.1-Mev level) reaction is considered in some detail and it is concluded that the experimental evidence is consistent with this reaction proceeding via the stripping mechanism near threshold.