Constraining the External Capture to the ${}^{16}\mathrm{O}$ Ground State and the $E2$ $S$ Factor of the ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ Reaction

The ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ reaction is one of the most crucial reactions in nuclear astrophysics. The $E2$ external capture to the ${}^{16}\mathrm{O}$ ground state (GS) has not been emphasized in previous analyses but may make a significant contribution to the ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ cross section depending on the value of the GS asymptotic normalization coefficient (ANC). In the present work, we determine this ANC to be $337\pm 45{\mathrm{fm}}^{-1/2}$ through the ${}^{12}\mathrm{C}({}^{11}\mathrm{B},{}^7\mathrm{Li}){}^{16}\mathrm{O}$ reaction using a high-precision magnetic spectrograph. This sheds light on the existing large discrepancy of more than 2 orders of magnitude between the previously reported ANC values. Based on the new ANC, we experimentally constrain the GS external capture and show that through interference with the high energy tail of the $2^{+}$ subthreshold state, a substantial enhancement in the GS $S_{E2}(300)$ factor can be obtained ($70\pm 7\mathrm{keV}\mathrm{b}$) compared to that of a recent review (45 keV b), resulting in an increase of the total $S$ factor from 140 to 162 keV b, which is now in good agreement with the value obtained by reproducing supernova nucleosynthesis calculations with the solar-system abundances. This work emphasizes that the external capture contribution for the ground state transition cannot be neglected in future analyses of the ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ reaction.

Figure 1

Focal-plane position spectrum of ${}^7\mathrm{Li}$ at ${\theta }_{\mathrm{lab}}=8°$ from the ${}^{12}\mathrm{C}({}^{11}\mathrm{B},{}^7\mathrm{Li}){}^{16}\mathrm{O}$ reaction. (a) Two-dimensional spectrum of energy vs focal-plane position. (b) Spectrum gated by the ${}^7\mathrm{Li}$ events in (a). The alpha, deuterons, and tritons are produced by the multibody breakup of the incident ${}^{11}\mathrm{B}$ ions on the ${}^{12}\mathrm{C}$ target.

Figure 2

Angular distribution of the ${}^{12}\mathrm{C}({}^{11}\mathrm{B},{}^7\mathrm{Li}){}^{16}\mathrm{O}$ reaction leading to the GS of ${}^{16}\mathrm{O}$. The black dashed-dotted line denotes the compound nucleus contribution.

Figure 3

Comparison of $R$-matrix calculations for the GS $E2$ component of the ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ reaction. The blue dashed line indicates the best fit $S$ factor from deBoer et al. [3], while the red solid and dashed lines indicate that of the present work as described in the text. The black data points represent those of Schürmann et al. [37], while the lower energy data of Fey [5], Schürmann et al. [37], Assunção et al. [38], Ouellet et al. [39], Kunz et al. [40], Redder et al. [41], Roters et al. [42], Makii et al. [43], and Plag et al. [44] are indicated by gray points. The vertical dotted line denotes the representative energy of astrophysical interest of $E_{\mathrm{c}.\mathrm{m}.}=300\mathrm{keV}$. The gray dashed-dotted lines indicate the range of uncertainty given only by the constraint of the $E2$ reaction data.

Figure 4

Comparison of recent values of the $2^{+}$ subthreshold ANC in ${}^{16}\mathrm{O}$ obtained from $R$-matrix fits to ${}^{12}\mathrm{C}(\alpha ,\alpha ){}^{12}\mathrm{C}$ data [47], ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ 6.92 MeV cascade data only [48] or global fitting [49], none of which include constraints on the ANCs from transfer measurements, or transfer reaction measurements using ${}^{12}\mathrm{C}({}^7\mathrm{Li},t){}^{16}\mathrm{O}$ [12, 13, 15, 45], ${}^{12}\mathrm{C}({}^6\mathrm{Li},d){}^{16}\mathrm{O}$ [12, 46], and ${}^{12}\mathrm{C}({}^{11}\mathrm{B},{}^7\mathrm{Li}){}^{16}\mathrm{O}$ [17] reactions. The red point indicates the value deduced from the present GS ANC of ${}^{16}\mathrm{O}$ and the low energy $E2$ capture data as discussed in the text. The blue and purple bands represent the weighted average of the ANCs from the $R$-matrix analyses including the present result and the one of the ANCs from six measurements of transfer reactions, respectively. See Table XIII of deBoer et al. [3] for comparisons to additional measurements that lack uncertainty estimates.