New measurement of the $\alpha$ asymptotic normalization coefficient of the ${1/2}^{+}$ state in ${}^{17}\mathrm{O}$ at 6.356 MeV that dominates the ${}^{13}\mathrm{C}(\alpha ,n){}^{16}\mathrm{O}$ reaction rate at temperatures relevant for the $s$ process

Background: Accurate knowledge of the ${}^{13}\mathrm{C}(\alpha ,n){}^{16}\mathrm{O}$ reaction cross section is important for the understanding of the $s$ process in asymptotic giant branch stars, since it is considered to be the main source of neutrons. The subthreshold $1/2^{+}$ state at excitation energy of 6.356 MeV in ${}^{17}\mathrm{O}$ has a strong influence on the reaction cross section at energies relevant for astrophysics. Several experiments have been performed to determine the contribution of this state to the ${}^{13}\mathrm{C}(\alpha ,n){}^{16}\mathrm{O}$ reaction rate. Nevertheless, significant discrepancies between different measurements remain.

Purpose: The aim of this work is to investigate these discrepancies.

Method: An 8 MeV ${}^{13}\mathrm{C}$ beam (below the Coulomb barrier) was used to study the $\alpha$-transfer reaction ${}^6\mathrm{Li}({}^{13}\mathrm{C},d){}^{17}\mathrm{O}$.

Results: The squared Coulomb-modified asymptotic normalization coefficient of the $1/2^{+}$ state in ${}^{17}\mathrm{O}$ measured in this work is ${\left({\tilde{C}}_{\alpha {-}^{13}\text{C}}^{{}^{17}\mathrm{O}(1/2+)}\right)}^2=3.6\pm 0.7{\text{fm}}^{-1}$.

Conclusions: Discrepancy between the results of $\alpha$-transfer experiments have been resolved. However, some discrepancy with the most recent measurement using the Trojan Horse method remains.

Figure 1

$\Delta E$ vs $E$ two-dimensional scatter plot observed by a pin detector at ${20}^{\circ }$ in the laboratory reference frame and used for particle identification. The typical deuteron cut is shown by the solid line.

Figure 2

Spectrum of deuterons from the ${}^6\mathrm{Li}({}^{13}\mathrm{C},d){}^{17}\mathrm{O}$ reaction at 8 MeV (7.72 MeV effective energy after energy-loss corrections) of ${}^{13}\mathrm{C}$ beam at ${144}^{\circ }$ in c.m.

Figure 3

Cross section and DWBA fit as a function of center-of-mass angle of the $1/2^{+}$ subthreshold resonance state of excitation energy 6.356 MeV in ${}^{17}\mathrm{O}$ measured in the present work (solid line) and in Ref. [5] (dashed line) by using a ${}^{13}\mathrm{C}$ beam energy of 7.72 and 7.81 MeV, respectively.

Figure 4

Squared Coulomb-modified ANC value obtained in this work, for the $1/2^{+}$ at excitation energy of 6.356 MeV in ${}^{17}\mathrm{O}$, compared with previous results from Johnson et al. [5], Pellegriti et al. [6], Cognata et al. [9], and Guo et al. [8].