Structural effects of ${}^{34}$Na in the ${}^{33}$Na(n,${\hat{I}}^3{)}^{34}$Na radiative capture reaction

Abstract

The path towards the production of \textit{r}-process seed nuclei follows a course where the neutron-rich light and medium mass nuclei play a crucial role. The neutron capture rates for these exotic nuclei could dominate over their $\hat{I}\pm$-capture rates, thereby enhancing their abundances at or near the drip line. We calculate the radiative neutron capture cross-section for the ${}^{33}$Na(n,${\hat{I}}^3{)}^{34}$Na reaction via the Coulomb dissociation of ${}^{34}$Na as it undergoes elastic breakup on ${}^{208}$Pb when directed at a beam energy of 100 MeV/u using the entirely quantum mechanical theory of finite range distorted wave Born approximation upgraded to incorporate deformation effects. The non-resonant one neutron radiative capture cross-section for ${}^{33}$Na(n,${\hat{I}}^3{)}^{34}$Na is calculated and is found to increase with increasing deformation of ${}^{34}$Na. An analytic scrutiny of the capture cross-section with neutron separation energy as a parameter is also done at different energy ranges. The calculated reaction rate is compared with the rate of the ${}^{33}$Na($\hat{I}\pm$,n)${}^{36}$Al reaction (deduced from the Hauser-Feshbach theory), and is found to be significantly higher below a temperature of $T_9=2$. Further, at the equilibrium temperature of $T_9=0.62$, the rate for the neutron capture had a small but non-negligible dependence on the structural parameters of ${}^{34}$Na. In addition, this neutron capture rate exceeded that of the $\hat{I}\pm$-capture reaction by orders of magnitude, indicating that the $\hat{I}\pm$-process should not break the (n,${\hat{I}}^3$) \textit{r-}process path at the ${}^{33}$Na isotope, thus, effectively pushing the abundance of sodium isotopes towards the neutron drip line.

14 pages, 9 figures