Evidence for nuclear molecular orbital effects in theC13+C13→C12+C14transfer reaction

Abstract

Detailed measurements of the angular distribution for the $^{13}\mathrm{C}$+$^{13}\mathrm{C}$\ensuremath{\rightarrow}$^{12}\mathrm{C}$+$^{14}\mathrm{C}$ single neutron transfer reaction as a function of bombarding energy from just above the Coulomb barrier to approximately four times the barrier energy are reported. The distorted-wave Born approximation for the transfer process does not reproduce the strong oscillations observed in both the experimental angular distributions and excitation functions, while analyses using a two-pole model for the transfer amplitude indicate significant multistep contributions. We show that the cross section in the 90\ifmmode^\circ\else\textdegree\fi{} region in the center of mass is characteristic of an increased collision delay time and of an effective $Q$ value 1 MeV smaller than the asymptotic observable $Q$ value. Angular distributions calculated using the dynamic two-center shell model of Konnecke et al. also succeed in reproducing the salient features of the data. The present experiment provides evidence for the occurrence of single-particle nuclear molecular behavior in a heavy-ion neutron transfer reaction. Data for the elastic scattering of $^{13}\mathrm{C}$+$^{13}\mathrm{C}$ are also presented and analyzed. We conclude that the elastic scattering excitation functions are consistent with the occurrence of orbiting in the dynamic interaction.NUCLEAR REACTIONS $^{13}\mathrm{C}$($^{13}\mathrm{C}$,$^{12}\mathrm{C}$)$^{14}\mathrm{C}$ and $^{13}\mathrm{C}$($^{13}\mathrm{C}$,$^{14}\mathrm{C}$)$^{12}\mathrm{C}$, measured $\ensuremath{\sigma}(E;\ensuremath{\theta})$, $E(\mathrm{lab})=16.0\ensuremath{-}50.0$ MeV, $\ensuremath{\theta}(\mathrm{lab})=17.8\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}51.4\ifmmode^\circ\else\textdegree\fi{}$, comparison with DWBA calculations, analysis using two-pole model, interpreted as evidence for reduced effective $Q$ value in the surface region and an increase in the collision delay time compared to values expected for a single step process; $^{13}\mathrm{C}$($^{13}\mathrm{C}$,$^{13}\mathrm{C}$)$^{13}\mathrm{C}$, measured $\ensuremath{\sigma}(E)$, $\ensuremath{\theta}(\mathrm{lab})=25\ifmmode^\circ\else\textdegree\fi{}, 30\ifmmode^\circ\else\textdegree\fi{}, 35\ifmmode^\circ\else\textdegree\fi{}, 40\ifmmode^\circ\else\textdegree\fi{}, 45\ifmmode^\circ\else\textdegree\fi{}$, $E(\mathrm{lab})=14.5\ensuremath{-}71.0$ MeV, optical model calculations, analysis using one pole model, gross structure oscillations interpreted as a geometrical effect.