Polology and (d, p) Reactions

Cross sections for ($d, p$) reactions calculated in the physical region are extrapolated to the Butler pole in order to investigate the possibility of extracting reduced widths. The cross sections are calculated by distorted-wave Born approximation. (DWBA), using a method of evaluation yielding cross sections with the correct analytic behavior near the pole. The cross sections in the unphysical region between the pole and the start of the physical region are calculated and compared with the extrapolation of cross sections from the physical region. Detailed calculations are made for two reactions in which the neutron is captured into an $s$ state: ${\mathrm{Si}}^{28}(d, p){\mathrm{Si}}^{29}$ to the ground state, and ${\mathrm{C}}^{12}(d, p){\mathrm{C}}^{13}$ (3.09 MeV). It is found that an effect of the Coulomb interaction prevents accurate extrapolation to the pole for heavy nuclei or low energies. The method of evaluating the DWBA cross section has an advantage over the usual method in that fewer partial waves need be summed.