Semiclassical calculations for the Gd156 (p,d) reaction

Abstract

Numerical semiclassical calculations are carried out to study the angular distribution of deuterons from the p,d pickup reaction of 25 MeV protons incident on the nucleus $^{156}\mathrm{Gd}$ and also its proton elastic scattering. It is found that, due to the rapid fall of the real optical potential in the vicinity of the target nucleus, the classical trajectories are very sensitive to the proton impact parameters. A selection of 276,983 trajectories is used for protons with impact parameters ${b}_{\mathrm{p}}$ satisfying $7.23018\phantom{\rule{0.16em}{0ex}}\mathrm{fm}\ensuremath{\le}{b}_{\mathrm{p}}\ensuremath{\le}10\phantom{\rule{0.16em}{0ex}}\mathrm{fm}$ with steps of ${10}^{\ensuremath{-}5}\phantom{\rule{0.16em}{0ex}}\mathrm{fm}$. Using the imaginary part of the optical potential for protons, a simple quantum approach is constructed to evaluate the probability of a surviving proton throughout its path. In addition, a simple three-body quantum approach is developed to calculate the probability of a neutron transfer by a surviving proton at closest approach. The formed deuteron is then allowed to start its trajectory while keeping its identity until detected. Throughout this journey, the deuteron trajectory is under the influence of its Coulomb and real optical potential, while its absorption is determined by the imaginary optical potential component. Within estimated uncertainties, the resulting theoretical angular distribution achieves a comparable fit with experimental results for the angular momentum transfer $\mathrm{L}=0$ compared to other theoretical models, and concludes that the strong p,d cross sections are due to the dominant ${\mathrm{s}}_{1/2}$ component of the Nilsson ${\frac{1}{2}}^{+}[400]$ level in $^{155}\mathrm{Gd}$.