Some ($d, \alpha$) Differential Cross Sections for ${\mathrm{Na}}^{23}$, ${\mathrm{Al}}^{27}$, and ${\mathrm{P}}^{31}$ at About 9.3 MeV

The differential cross sections for ($d, \alpha$) reactions which lead to various nuclear states in ${\mathrm{Ne}}^{21}$ (ground, 1, and 2), ${\mathrm{Mg}}^{25}$ (ground, 1, 2, 3, and 4), and ${\mathrm{Si}}^{29}$ (ground, 1, 2, 3, 4, 5, and 6) were measured at nominal deuteron energies of 9.2, 9.2, and 9.5 MeV, respectively, using a silicon surface-barrier detector. Targets of various thicknesses ranging from 70 to 642 μg/${\mathrm{cm}}^2$ were used. In each case the differential cross section was determined at more than 34 angles from 10 to 172.5°. Although the shape of each angular distribution is different from any of the others in detail, all exhibit the following characteristics: pronounced forward and backward peaking; an over-all oscillatory structure; an asymmetry about 90°; and minima whose magnitudes differ significantly from zero. Comparisons are made with ($d, \alpha$) results which have been previously obtained by other investigators using deuteron energies in the 7-15-MeV range. No correlation could be established between any specific detail in shape or general feature of these angular distributions and any physical quantity associated with the nuclear states involved. Analyses of these differential cross sections are described using an expression consisting of the sum of an isotropic component and a plane-wave Born approximation component which arises from the coherent action of a two-nucleon pickup and a heavy-particle-stripping mechanism.