Mechanism of theMg26(O18,O16)Mg28reaction atEO18=50MeV and the energy levels ofMg28

Abstract

The reaction $^{26}\mathrm{Mg}$($^{18}\mathrm{O}$, $^{16}\mathrm{O}$)$^{28}\mathrm{Mg}$ has been studied at a bombarding energy of 50 MeV between laboratory angles of 4\ifmmode^\circ\else\textdegree\fi{} and 17\ifmmode^\circ\else\textdegree\fi{}. The differential cross sections of the lowest four states of $^{28}\mathrm{Mg}$ have been compared to exact finite-range calculations in the distorted-wave Born approximation and coupled-channels Born approximation formulations. The reaction-mechanism calculations employed wave functions for the initial and final nuclear states which were generated in shell-model calculations carried out in the full ${d}_{\frac{5}{2}}\ensuremath{-}{s}_{\frac{1}{2}}\ensuremath{-}{d}_{\frac{3}{2}}$ basis space. The relative importance of one-step and two-step processes in the population of the different final states is evaluated and the effectiveness of current reaction theories in accounting for phenomena such as are exemplified by the present data is discussed.NUCLEAR REACTIONS $^{26}\mathrm{Mg}$($^{18}\mathrm{O}$, $^{16}\mathrm{O}$)$^{28}\mathrm{Mg}$; enriched target, $E=50$ MeV, measured $\ensuremath{\sigma}(\ensuremath{\theta})$, microscopic DWBA and CCBA analysis with shell-model wave functions; deduced levels of $^{28}\mathrm{Mg}$.