Neutron capture cross sections of light neutron-rich nuclei relevant for $r$-process nucleosynthesis

The measurements of neutron capture cross sections of neutron-rich nuclei are challenging but essential for understanding nucleosynthesis and stellar evolution processes in the explosive burning scenario. In the quest of $r$-process abundances, according to the neutrino-driven-wind model, light neutron-rich unstable nuclei may play a significant role as seed nuclei that influence the abundance pattern. Hence, experimental data for neutron capture cross sections of neutron-rich nuclei are needed. Coulomb dissociation of radioactive ion beams at intermediate energy is a powerful indirect method for inferring capture cross section. As a test case for validation of the indirect method, the neutron capture cross section ($n$, $\gamma$) for ${}^{14}\mathrm{C}$ was inferred from the Coulomb dissociation of ${}^{15}\mathrm{C}$ at intermediate energy ($600A$ MeV). A comparison between different theoretical approaches and experimental results for the reaction is discussed. We report for the first time experimental reaction cross sections of ${}^{28}\mathrm{Na}(n,\gamma ){}^{29}\mathrm{Na}$, ${}^{29}\mathrm{Na}(n,\gamma ){}^{30}\mathrm{Na}$, ${}^{32}\mathrm{Mg}(n,\gamma ){}^{33}\mathrm{Mg}$, and ${}^{34}\mathrm{Al}(n,\gamma ){}^{35}\mathrm{Al}$. The reaction cross sections were inferred indirectly through Coulomb dissociation of ${}^{29,30}\mathrm{Na}$, ${}^{33}\mathrm{Mg}$, and ${}^{35}\mathrm{Al}$ at incident projectile energies around 400–430 $A$ MeV using the FRS-LAND setup at GSI, Darmstadt. The neutron capture cross sections were obtained from the photoabsorption cross sections with the aid of the detailed balance theorem. The reaction rates for the neutron-rich Na, Mg, Al nuclei at typical $r$-process temperatures were obtained from the measured ($n,\gamma$) capture cross sections. The measured neutron capture reaction rates of the neutron-rich nuclei, ${}^{28}\mathrm{Na}$, ${}^{29}\mathrm{Na}$, and ${}^{34}\mathrm{Al}$ are significantly lower than those predicted by the Hauser-Feshbach decay model. A similar trend was observed earlier for ${}^{17}\mathrm{C}$ and ${}^{19}\mathrm{N}$ but in the case of ${}^{14}\mathrm{C}(n,\gamma ){}^{15}\mathrm{C}$ the trend is opposite. The situation is more complicated when the ground state has a multi-particle-hole configuration. For ${}^{32}\mathrm{Mg}$, the measured cross section is about $40\text{–}90\%$ higher than the Hauser-Feshbach prediction.

Figure 1

(Top) Identification plot for a mixed radioactive beam impinging on the secondary targets. (Bottom) Charge distribution of the outgoing fragments. Figure reprinted from [43], copyright by Institute of Physics, 2017.

Figure 2

Variation of number of virtual photons of $E1$ type with energy $E_{\gamma }$ obtained from an ${}^{30}\mathrm{Na}$ beam with an energy of $430A$ MeV incident on a ${}^{208}\mathrm{Pb}$ target.

Figure 3

The data show invariant mass spectrum of ${}^{29}\mathrm{Na}$ breaking into ${}^{28}\mathrm{Na}$ (2.7 MeV) and one neutron against excitation energy ($E^{*}$). Lines in three panels represent the fitted direct breakup model calculations folded with instrumental response where the valence neutron is occupying the $s$, the $p$ and the $d$ orbital, respectively. The model estimations are normalized with the fitted spectroscopic factors. The shaded regions represent the errors of those.

Figure 4

The data show the invariant mass spectrum of ${}^{30}\mathrm{Na}$ breaking into ${}^{29}\mathrm{Na}$ (1.25 MeV) and one neutron against $E^{*}$. The line in the top and bottom panels represents the DB calculation using the $p$ and the $d$ wave for the valence neutron, respectively. The method of fitting was the same as described in Fig. 3.

Figure 5

(Top) The data represent the invariant mass spectrum of ${}^{35}\mathrm{Al}$ breaking into ${}^{34}\mathrm{Al}$ (2.5 MeV) and one neutron against $E^{*}$. The line at top and bottom panels shows the DB model predictions where the valence neutron is occupying the $f$ and the $p$ orbital, respectively. The fitting procedure is same as described in Fig. 3.

Figure 6

Variation of photoabsorption cross sections with the excitation energy for ${}^{29}\mathrm{Na}(\gamma ,n){}^{28}\mathrm{Na}$ (top), ${}^{30}\mathrm{Na}(\gamma ,n){}^{29}\mathrm{Na}$ (bottom).

Figure 7

Photoabsorption cross sections with variation of the excitation energy for ${}^{33}\mathrm{Mg}(\gamma ,n){}^{32}\mathrm{Mg}$ (top) and ${}^{35}\mathrm{Al}(\gamma ,n){}^{34}\mathrm{Al}$ (bottom).

Figure 8

Plot of $\sigma (n,\gamma$) $E^{-1/2}$ as a function of relative energy between ${}^{14}\mathrm{C}$ and neutron, $E_{\mathrm{c}.\mathrm{m}.}$ obtained from different direct and indirect methods, as well as from calculations.

Figure 9

Variation of reaction rates in ${\mathrm{cm}}^3{\mathrm{mol}}^{-1}{\mathrm{s}}^{-1}$ with temperature $T_9$ for ${}^{14}\mathrm{C}(n,\gamma ){}^{15}\mathrm{C}$ obtained from both CD data [34] and Hauser-Feshbach calculation [75].

Figure 10

Neutron capture cross sections as a function of neutron energy $E_n$ for ${}^{28}\mathrm{Na}(n,\gamma ){}^{29}\mathrm{Na}$ (top), ${}^{29}\mathrm{Na}(n,\gamma ){}^{30}\mathrm{Na}$ (bottom).

Figure 11

Variation of the neutron capture cross sections with neutron energy $E_n$ for ${}^{32}\mathrm{Mg}(n,\gamma ){}^{33}\mathrm{Mg}$ (top) and ${}^{34}\mathrm{Al}(n,\gamma ){}^{35}\mathrm{Al}$ (bottom).

Figure 12

Variation of reaction rates in ${\mathrm{cm}}^3{\mathrm{mol}}^{-1}{\mathrm{s}}^{-1}$ with temperature $T_9$ for ${}^{28}\mathrm{Na}(n,\gamma ){}^{29}\mathrm{Na}$ (top), ${}^{29}\mathrm{Na}(n,\gamma ){}^{30}\mathrm{Na}$ (bottom). The measured reaction rates (represented by the shaded region) have been compared with Hauser-Feshbach estimates (represented by a dot-dashed line) [75].

Figure 13

Variation of reaction rates in ${\mathrm{cm}}^3{\mathrm{mol}}^{-1}{\mathrm{s}}^{-1}$ with temperature $T_9$ for ${}^{32}\mathrm{Mg}(n,\gamma ){}^{33}\mathrm{Mg}$ (top) and ${}^{34}\mathrm{Al}(n,\gamma ){}^{35}\mathrm{Al}$ (bottom). The measured reaction rates (shaded region) have been compared with Hauser-Feshbach estimates dot-dashed line) [75].