Measurement of elastic ${}^{12}$C $+$ $\alpha$ scattering: Above the proton separation energy

Background: Reactions that probe the compound nucleus structure of ${}^{16}$O near the $\alpha$ and proton separation energies have important implications for nuclear astrophysics. New, more sensitive measurements of the reaction ${}^{15}$N${(p,\gamma )}^{16}$O have motivated the need for improved compound-nucleus reaction data in other channels. A previous work [P. Tischhauser et al., Phys. Rev. C 79, 055803 (2009)] reported extensive $\alpha$-scattering data over the energy region from $E_{\alpha }=2.6$ to $E_{\alpha }=6.6$ MeV. During this experiment data for higher energies, from $E_{\alpha }=6.6$ to $E_{\alpha }=8.2$ MeV, were also recorded but were not analyzed. The unpublished data cover the excitation energy range from the proton separation energy at $E_x$ $=$ 12.13 MeV up to 13.31 MeV, the same energy range important for the reaction ${}^{15}$N${(p,\gamma )}^{16}$O.

Purpose: These previously unpublished data for ${}^{12}$C${(\alpha ,\alpha )}^{12}$C as well as the reactions ${}^{12}$C${(\alpha ,{\alpha }_1)}^{12}$C and ${}^{12}$C${(\alpha ,p)}^{15}$N are analyzed in order to provide additional data for a comprehensive $R$-matrix analysis of compound-nucleus reactions populating ${}^{16}$O.

Methods: Expanding on the previous publication's analysis, the ratio of the reaction yields was analyzed using a multiple-channel $R$-matrix calculation.

Results: The excitation curves resolved resonances at $E_{\alpha }$ ($J^{\pi })=7.05(1^{-}$), 7.75 (2${}^{+}$), 7.91 (1${}^{-}$), 7.97 (3${}^{-}$), and 8.13 (3${}^{-}$) MeV. The $R$-matrix analysis revealed excellent agreement between the measured yield ratios and cross-section data from the literature. The two 1${}^{-}$ levels at $E_{\alpha }=7.05$ and 7.91 MeV are those that dominate the ${}^{15}$N${(p,\gamma )}^{16}$O cross section.

Conclusions: In a future publication, the additional constraints provided by these data will be used in a comprehensive multiple-channel $R$-matrix analysis to investigate the low-energy cross section of the reaction ${}^{15}$N${(p,\gamma )}^{16}$O.

Figure 1

Fits to the ${}^{12}$C${(\alpha ,{\alpha }_0)}^{12}$C differential cross-section data of Ref. [9] at ${\theta }_{\mathrm{lab}}=71.{55}^{\circ }$ (a), 104.5${}^{\circ }$ (b), 106.6${}^{\circ }$ (c), 124.89${}^{\circ }$ (d), 136.06${}^{\circ }$ (e), and 167${}^{\circ }$ (f).

Figure 2

Fits to the phase shifts from Ref. [11] for $l=0$ (a), 1 (b), 2 (c), 3 (d), 4 (e), and 5 (f) included in the $R$-matrix analysis.

Figure 3

Fits to the ${}^{12}$C${(\alpha ,{\alpha }_0)}^{12}$C yield data of this work at ${\theta }_{\mathrm{lab}}=24.0^{\circ }$ (a), 33.9${}^{\circ }$ (b), 38.9${}^{\circ }$ (c), 43.9${}^{\circ }$ (d), 48.9${}^{\circ }$ (e), 54.0${}^{\circ }$ (f), 63.9${}^{\circ }$ (g), and 68.9${}^{\circ }$ (h). The $R$-matrix fit was performed simultaneously with previous data from the literature.

Figure 4

Fits to the ${}^{12}$C${(\alpha ,{\alpha }_0)}^{12}$C yield data of this work at ${\theta }_{\mathrm{lab}}=74.0^{\circ }$ (a), 75.8${}^{\circ }$ (b), 80.8${}^{\circ }$ (c), 84.0${}^{\circ }$ (d), 85.8${}^{\circ }$ (e), 89.0${}^{\circ }$ (f), 90.8${}^{\circ }$ (g), and 94.0${}^{\circ }$ (h). The $R$-matrix fit was performed simultaneously with previous data from the literature.

Figure 5

Fits to the ${}^{12}$C${(\alpha ,{\alpha }_0)}^{12}$C yield data of this work at ${\theta }_{\mathrm{lab}}=95.8^{\circ }$ (a), 99.0${}^{\circ }$ (b), 100.8${}^{\circ }$ (c), 103.9${}^{\circ }$ (d), 105.8${}^{\circ }$ (e), 110.8${}^{\circ }$ (f), 115.8${}^{\circ }$ (g), and 120.8${}^{\circ }$ (h). The $R$-matrix fit was performed simultaneously with previous data from the literature.

Figure 6

Fits to the ${}^{12}$C${(\alpha ,{\alpha }_0)}^{12}$C yield data of this work at ${\theta }_{\mathrm{lab}}=125.8^{\circ }$ (a), 130.8${}^{\circ }$ (b), 140.8${}^{\circ }$ (c), 150.8${}^{\circ }$ (d), 160.8${}^{\circ }$ (e), and 165.9${}^{\circ }$ (f). The $R$-matrix fit was performed simultaneously with previous data from the literature.

Figure 7

Fits to the previously unpublished ${}^{12}$C${(\alpha ,{\alpha }_1)}^{12}$C differential yields of this work at ${\theta }_{\mathrm{lab}}=24.0^{\circ }$ (a), 33.9${}^{\circ }$ (b), 38.9${}^{\circ }$ (c), 43.9${}^{\circ }$ (d), 63.9${}^{\circ }$ (e), 68.9${}^{\circ }$ (f), 74.0${}^{\circ }$ (g), and 79.0${}^{\circ }$ (h). The $(\alpha ,{\alpha }_1)$ yields were divided by the corresponding $(a,a_0)$ yields. The $R$-matrix fit was performed simultaneously with previous data from the literature.

Figure 8

Fits to the previously unpublished ${}^{12}$C${(\alpha ,{\alpha }_1)}^{12}$C differential yields of this work at ${\theta }_{\mathrm{lab}}=80.8^{\circ }$ (a), 84.0${}^{\circ }$ (b), 85.8${}^{\circ }$ (c), 89.0${}^{\circ }$ (d), 90.8${}^{\circ }$ (e), 94.0${}^{\circ }$ (f), 95.8${}^{\circ }$ (g), and 99.0${}^{\circ }$ (h). The $(\alpha ,{\alpha }_1)$ yields were divided by the corresponding $(a,a_0)$ yields. The $R$-matrix fit was performed simultaneously with previous data from the literature.

Figure 9

Fits to the previously unpublished ${}^{12}$C${(\alpha ,p)}^{15}$N differential yields of this work at ${\theta }_{\mathrm{lab}}=24.0^{\circ }$ (a), 33.9${}^{\circ }$ (b), 38.9${}^{\circ }$ (c), 43.9${}^{\circ }$ (d), 48.9${}^{\circ }$ (e), 54.0${}^{\circ }$ (f), 68.9${}^{\circ }$ (g), and 74.0${}^{\circ }$ (h). The $(\alpha ,p)$ yields were divided by the corresponding $(a,a_0)$ yields. The $R$-matrix fit was performed simultaneously with previous data from the literature.

Figure 10

Fits to the previously unpublished ${}^{12}$C${(\alpha ,p)}^{15}$N differential yields of this work at ${\theta }_{\mathrm{lab}}=79.0^{\circ }$ (a), 80.8${}^{\circ }$ (b), 84.0${}^{\circ }$ (c), 85.8${}^{\circ }$ (d), 89.0${}^{\circ }$ (e), 90.8${}^{\circ }$ (f), 94.0${}^{\circ }$ (g), and 95.8${}^{\circ }$ (h). The $(\alpha ,p)$ yields were divided by the corresponding $(a,a_0)$ yields. The $R$-matrix fit was performed simultaneously with previous data from the literature.

Figure 11

Fits to the previously unpublished ${}^{12}$C${(\alpha ,p)}^{15}$N differential yields of this work at ${\theta }_{\mathrm{lab}}=99.0^{\circ }$ (a), 100.8${}^{\circ }$ (b), 103.9${}^{\circ }$ (c), 105.8${}^{\circ }$ (d), 110.8${}^{\circ }$ (e), 115.8${}^{\circ }$ (f), 120.8${}^{\circ }$ (g), and 125.8${}^{\circ }$ (h). The $(\alpha ,p)$ yields were divided by the corresponding $(a,a_0)$ yields. The $R$-matrix fit was performed simultaneously with previous data from the literature.

Figure 12

Fits to the previously unpublished ${}^{12}$C${(\alpha ,p)}^{15}$N differential yields of this work at ${\theta }_{\mathrm{lab}}=130.8^{\circ }$ (a), 140.8${}^{\circ }$ (b), 150.8${}^{\circ }$ (c), and 160.8${}^{\circ }$ (d). The $(\alpha ,p)$ yields were divided by the corresponding $(a,a_0)$ yields. The $R$-matrix fit was performed simultaneously with previous data from the literature.