Neutron capture rates of ${}^{18}\mathrm{C}$

Background: Small changes in reaction rates due to neutron capture, $\alpha$ capture, and $\beta$ decay by exotic nuclei in the low and medium mass region can direct the $r$-process path in different ways, thereby affecting the abundance pattern. In this context, it is important to find the most abundant carbon isotope closer to the neutron drip line. It was postulated that the $(n,\gamma )$ reaction network will be broken at the ${}^{18}\mathrm{C}$ isotope and follow the ${}^{18}\mathrm{C}(\alpha ,n){}^{21}\mathrm{O}$ reaction path [Terasawa et al., Astrophys. J. 562, 470 (2001)].

Purpose: In this paper, we calculate the radiative capture cross section of ${}^{18}\mathrm{C}(n,\gamma ){}^{19}\mathrm{C}$, taking into consideration the halo character of ${}^{19}\mathrm{C}$. Eventually, we calculate the reaction rate for the same reaction and compare it with Hauser-Feshbach estimates of $(n,\gamma )$ and $(\alpha ,n)$ to determine the abundance pattern of carbon isotopes.

Method: We compute the relative energy spectrum for elastic Coulomb breakup of ${}^{19}\mathrm{C}$ on a Pb target at a beam energy of 67 MeV/u using the finite-range distorted-wave Born approximation (FRDWBA) theory. We use the principle of detailed balance to calculate the radiative capture cross section from the photo disintegration cross section, and subsequently we calculate the reaction rate.

Results: We report the ${}^{18}\mathrm{C}(n,\gamma ){}^{19}\mathrm{C}$ capture cross section as a function of relative energy. Estimation of the energy range contributing to the reaction rates is done by calculating the integrand of the reaction rate expression. A comparison of the ${}^{18}\mathrm{C}(n,\gamma ){}^{19}\mathrm{C}$ with ${}^{18}\mathrm{C}(\alpha ,n){}^{21}\mathrm{O}$ (extracted from the Hauser-Feshbach estimates) shows the domination of the neutron radiative capture reaction in the relevant temperature range $T_9=0.1–4$.

Conclusion: The radiative capture cross section of ${}^{18}\mathrm{C}$ calculated using FRDWBA theory agrees well with the experimental data, whereas the statistical model calculation lies orders of magnitude lower. We conclude that at equilibrium temperature of $T_9=0.62$, the ${}^{18}\mathrm{C}(n,\gamma ){}^{19}\mathrm{C}$ reaction rate is orders of magnitude higher than that of the ${}^{18}\mathrm{C}(\alpha ,n){}^{21}\mathrm{O}$ reaction, thereby pushing the carbon isotope abundance towards the neutron drip line.

Figure 1

The relative energy spectra obtained in the elastic Coulomb breakup of ${}^{19}\mathrm{C}$ on ${}^{208}\mathrm{Pb}$ at 67 MeV/u. The solid line represents FRDWBA calculation and the experimental data are shown by solid circles (taken from Ref. [24]). The inset shows the spectra up to a relative energy of 1 MeV.

Figure 2

Comparison of ${}^{18}\mathrm{C}(n,\gamma ){}^{19}\mathrm{C}$ capture cross sections. The solid line shows the FRDWBA calculations while the dashed line represents the H-F calculation of Ref. [10]. The solid circles are developed from the relative energy spectrum taken from Ref. [24], while the dot-dashed curve (showing the capture cross section obtained from the experimental relative energy spectrum) is reproduced from Ref. [10]. For more details, see text.

Figure 3

Integrand of the reaction rate equation [Eq. (7)] as a function of the relative energy for the ${}^{18}\mathrm{C}(n,\gamma ){}^{19}\mathrm{C}$ reaction using the FRDWBA theory (solid line) and the cross section extracted from Ref. [10] (dot-dashed line), at a temperature of $T_9=1$.

Figure 4

Comparison of ${}^{18}\mathrm{C}(n,\gamma ){}^{19}\mathrm{C}$ reaction rates. The solid and the dot-dashed lines correspond to the FRDWBA computations and the rate obtained from the cross section extracted from Ref. [10], respectively. The rates from the standard rate equation (Ref. [10]) and the H-F estimates are displayed by the dotted and dashed lines, respectively. The ${}^{18}\mathrm{C}(\alpha ,n){}^{21}\mathrm{O}$ reaction rate is represented by the double-dot–dashed line and is seen to be much lower than the ${}^{18}\mathrm{C}(n,\gamma ){}^{19}\mathrm{C}$ rates for $T_9<3$. For more details, see text.