Reaction rate for carbon burning in massive stars

Carbon burning is a critical phase for nucleosynthesis in massive stars. The conditions for igniting this burning stage, and the subsequent isotope composition of the resulting ashes, depend strongly on the reaction rate for ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion at very low energies. Results for the cross sections for this reaction are influenced by various backgrounds encountered in measurements at such energies. In this paper, we report on a new measurement of ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion cross sections where these backgrounds have been minimized. It is found that the astrophysical $S$ factor exhibits a maximum around $E_{\mathrm{cm}}=3.5–4.0$ MeV, which leads to a reduction of the previously predicted astrophysical reaction rate.

Figure 1

$S$ factors from previous measurements of the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion reaction. Charged-particle detection was used in the measurements by Patterson, Mazarakis, Becker and Zickefoose, while $\gamma$-ray detection was employed in the measurements of High, Barron-Palos, Auguilera and Spillane [4, 5, 6, 7, 8, 9, 10, 11].

Figure 2

A schematic drawing of the experimental setup showing the spherical target chamber mounted in the middle of the Gammasphere array.

Figure 3

(a) Particle-$\gamma$ coincidence events detected by DSSD1 located at backward angles at the second lowest energy studied in this experiment, $E_{\mathrm{cm}}=2.84$ MeV. (b) Energy-angle correlation of the coincident particle-$\gamma$ events shown in the rectangular region in (a). The dashed line represents the kinematic locus expected for the ${}^{12}\mathrm{C}({}^{12}\mathrm{C},p){}^{23}\mathrm{Na}$ reaction populating the 0.440-MeV state in ${}^{23}\mathrm{Na}$. Panels (c) and (d) show plots similar to (a) and (b), but measured for the third lowest energy, $E_{\mathrm{cm}}=2.96$ MeV. The dashed lines represent the kinematic locus expected for the ${}^{12}\mathrm{C}({}^{12}\mathrm{C},\alpha ){}^{20}\mathrm{Ne}$ and ${}^{12}\mathrm{C}({}^{12}\mathrm{C},p){}^{23}\mathrm{Na}$ reactions. See text for details.

Figure 4

Black points: $S$ factors from the present measurements of the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ fusion reaction. Magenta and green stars: results from the recent measurement of the same system in Refs. [10] and [11], respectively. The insert gives an enlarged plot in the region near 2.7 MeV. The light blue, magenta dashed, black, and red lines are calculations explained in the text.

Figure 5

$S$ factors for the systems ${}^{28}\mathrm{Si}+{}^{30}\mathrm{Si}$ (a), ${}^{27}\mathrm{Al}+{}^{45}\mathrm{Sc}$ (b), ${}^{24}\mathrm{Mg}+{}^{30}\mathrm{Si}$ (c), and ${}^{28}\mathrm{Si}+{}^{64}\mathrm{Ni}$ (d). The fusion $Q$ values are 14.3, 9.63, 17.89, and $-1.87$ MeV, respectively. The various lines are the result of calculations discussed in the text.

Figure 6

Astrophysical reaction rates calculated from the experimental data and extrapolations in Fig. 4. The bands for Spillane and for Zichefoose represent the experimental uncertainties of experimental the cross sections.