Structural effects of $^{34}$Na in the $^{33}$Na(n,$γ)^{34}$Na radiative capture reaction

Abstract

Background: The path towards the production of 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 α-capture rates, thereby enhancing their abundances at or near the drip line. Sodium isotopes especially should have a strong neutron capture flow to gain abundance at the drip line. In this context, study of 33 Na(n,γ) 34 Na and 33 Na(α,n) 36 Al reactions becomes indispensable.Purpose: In this paper, we calculate the radiative neutron capture cross-section for the 33 Na(n,γ) 34 Na reaction involving deformation effects. Subsequently, the rate for this reaction is found and compared with that of the α-capture for the 33 Na(α,n) 36 Al reaction to determine the possible path flow for the abundances of sodium isotopes.Method: We use the entirely quantum mechanical theory of finite range distorted wave Born approximation upgraded to incorporate deformation effects, and calculate 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 principle of detailed balance to study the reverse photodisintegration reaction, we find the radiative neutron capture cross-section with variation in one neutron binding energy and quadrupole deformation of 34 Na. The rate of this 33 Na(n,γ) 34 Na reaction is then compared with that of the α-capture by 33 Na deduced from the Hauser-Feshbach theory. Results:The non-resonant one neutron radiative capture cross-section for 33 Na(n,γ) 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(α,n) 36 Al reaction, and is found to be significantly higher below a temperature of T9 = 2. Conclusion:At the equilibrium temperature of T9 = 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 α-capture reaction by orders of magnitude, indicating that the α-process should not break the (n,γ) r-process path at 33 Na isotope, thus, effectively pushing the abundance of sodium isotopes towards the neutron drip line.