Recoil Angular Distributions of theLi6(d, n)Be7andC12(d, n)N13Reactions

Abstract

The reactions $^{6}\mathrm{Li}(d, n)^{7}\mathrm{Be}$ (g.s.+0.431 MeV) and $^{12}\mathrm{C}(d, n)^{13}\mathrm{N}$ (g.s.) have been studied by recoil spectrometry at bombarding energies of 12, 15, and 17 MeV. The recoils were detected by a solid-state detector in coincidence with the neutrons detected by a plastic scintillator. Experimental absolute differential cross sections at the three bombarding energies are given for both reactions. Also given are the excitation functions over the energy region 12-17 MeV at about 60\ifmmode^\circ\else\textdegree\fi{} recoil c.m. angle for both reactions, and for the reaction $^{19}\mathrm{F}(d, n)^{20}\mathrm{Ne}$ (g.s.). The $^{6}\mathrm{Li}$ and $^{12}\mathrm{C}$ reactions were analyzed in the distorted-wave Born approximation (DWBA), taking into account the effects of spin-orbit force, finite range, and nonlocality corrections. The agreement between the experimental and theoretical angular distributions is good for the $^{6}\mathrm{Li}$ reaction, and the agreement for the $^{12}\mathrm{C}$ reaction is fair at 17 MeV. The excitation functions for the two reactions are relatively smooth. The experimental absolute differential cross sections for the $^{6}\mathrm{Li}$ reaction agree fairly well with the theoretical cross sections obtained by incorporating the spectroscopic factors from recent shell-model calculations. For the $^{12}\mathrm{C}$ reaction, the spectroscopic factor extracted from the experimental cross section agrees well with the theoretical value at 17 MeV. The experimental cross sections at 12 and 15 MeV are higher than the theoretical estimates; some possible explanations are discussed. The ratios of the experimental to the theoretical cross sections as a function of bombarding energy follow the same trend as for the reaction $^{12}\mathrm{C}(d, p)^{13}\mathrm{C}$ (g.s.). An evaluation of the technique of recoil spectrometry for studying ($d, n$) and other nuclear reactions is given.