Deep Underground Laboratory Measurement of ${}^{13}\mathrm{C}(\alpha ,n){}^{16}\mathrm{O}$ in the Gamow Windows of the $s$ and $i$ Processes

The ${}^{13}\mathrm{C}(\alpha ,n){}^{16}\mathrm{O}$ reaction is the main neutron source for the slow-neutron-capture process in asymptotic giant branch stars and for the intermediate process. Direct measurements at astrophysical energies in above-ground laboratories are hindered by the extremely small cross sections and vast cosmic-ray-induced background. We performed the first consistent direct measurement in the range of $E_{\mathrm{c}.\mathrm{m}.}=0.24$ to 1.9 MeV using the accelerators at the China Jinping Underground Laboratory and Sichuan University. Our measurement covers almost the entire intermediate process Gamow window in which the large uncertainty of the previous experiments has been reduced from 60% down to 15%, eliminates the large systematic uncertainty in the extrapolation arising from the inconsistency of existing datasets, and provides a more reliable reaction rate for the studies of the slow-neutron-capture and intermediate processes along with the first direct determination of the alpha strength for the near-threshold state.

Figure 1

The $S$ factor of the ${}^{13}\mathrm{C}(\alpha ,n){}^{16}\mathrm{O}$ reaction. The uncertainties from the fit to the $\mathrm{JUNA}+\mathrm{SCU}$ data are indicated by dotted lines. The best fit and lower limit recommended by LUNA [7] are shown as black and blue dashed lines, respectively. The $S$ factors have been corrected with the screening potential $U_e=0.78\mathrm{keV}$. The temperatures in $T_9$ on the top correspond to the center energy of the Gamow window on the bottom.

Figure 2

The Gamow function of ${}^{13}\mathrm{C}(\alpha ,n){}^{16}\mathrm{O}$ at $T_9=0.1$ and 0.2. Color coding is identical to Fig. 1.

Figure 3

Selected reaction rates normalized by the rate determined in this work. The uncertainties of our new rate [43] and the LUNA rate, based on their best fit, are indicated by the red hatched area and yellow shaded area, respectively. For comparison, we also show the rates from NACRE-II [56], LUNA [7], and JINA Reaclib [5, 57].