Measurement and Distorted-Wave Born-Approximation Analyses of the 18.7-MeV Cross Sections for theNa23(α,d0,1)Mg25Reactions

Abstract

The 18.7-MeV differential cross sections for the ${\mathrm{Na}}^{23}(\ensuremath{\alpha},{d}_{0,1}){\mathrm{Mg}}^{25}$ reactions were determined at 5\ifmmode^\circ\else\textdegree\fi{} intervals over the angular range from about 25\ifmmode^\circ\else\textdegree\fi{} to 170\ifmmode^\circ\else\textdegree\fi{}. The spectrometer system included an ($E\ifmmode\times\else\texttimes\fi{}\ensuremath{\Delta}E$) particle identifier, an ($E,\ensuremath{\Delta}E$) counter telescope consisting of two silicon surface-barrier detectors, and a multichannel pulse-height analyzer. One target each of sodium hydride (266\ifmmode\pm\else\textpm\fi{}10 \ensuremath{\mu}g/${\mathrm{cm}}^{2}$) and metallic sodium (267\ifmmode\pm\else\textpm\fi{}10 \ensuremath{\mu}g/${\mathrm{cm}}^{2}$) was used. The target material was vaporized in a vacuum and condensed onto a thin (\ensuremath{\sim}20 \ensuremath{\mu}g/${\mathrm{cm}}^{2}$) Formvar substrate. The integrated cross sections for the transitions to the ground and 0.584-MeV states of ${\mathrm{Mg}}^{25}$ are 1377\ifmmode\pm\else\textpm\fi{}30 \ensuremath{\mu}b (23.1\ifmmode^\circ\else\textdegree\fi{} to 171.6\ifmmode^\circ\else\textdegree\fi{}) and 349\ifmmode\pm\else\textpm\fi{}9 \ensuremath{\mu}b (34.7\ifmmode^\circ\else\textdegree\fi{} to 171.6\ifmmode^\circ\else\textdegree\fi{}), respectively. The angular distributions are similar in over-all shape and exhibit a somewhat washed-out structure with strong backward-angle peaking. This similarity could not be correlated in a simple way with any of the known properties of the nuclear states. Distorted-wave Born-approximation analyses of the data have been made in terms of both zero-range knockout and zero-range stripping models. In the knockout model, the initial (final) nuclear state is described as a two-body system consisting of a deuteron (an $\ensuremath{\alpha}$ particle) bound to a ${\mathrm{Ne}}^{21}$ core, and in the stripping model the final nuclear state is described as a deuteron bound to a ${\mathrm{Na}}^{23}$ core. Using reasonable parameter values, the gross features of both angular distributions could be marginally reproduced by the knockout model but not by the stripping model. The knockout analyses require a $1{g}_{\frac{3}{2}}$ state for the ($d,{\mathrm{Ne}}^{21}$) system representing the ground state of ${\mathrm{Na}}^{23}$, and require $2{d}_{\frac{5}{2}}$ and $2{d}_{\frac{1}{2}}$ states for the ($\ensuremath{\alpha},{\mathrm{Ne}}^{21}$) system representing the ground and 0.584-MeV states of ${\mathrm{Mg}}^{25}$, respectively.