Direct and indirect $\alpha$ transfer in elastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ scattering

The extensive elastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ scattering data measured at low energies show consistently an oscillating enhancement of the elastic cross section at backward angles that is difficult to describe within the conventional optical model. Given the significant $\alpha$ spectroscopic factors predicted for the dissociation ${}^{16}\mathrm{O}\to \alpha +{}^{12}\mathrm{C}$ by the shell model (SM) and $\alpha$-cluster model calculations, the contribution of the $\alpha$ transfer channels to the elastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ scattering should not be negligible, and is expected to account for the enhanced oscillation of the elastic cross section at backward angles. To reveal the impact of the $\alpha$ transfer, a systematic coupled reaction channels (CRCs) analysis of the elastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ scattering has been performed where the multistep couplings between the elastic and inelastic scattering channels and the direct and indirect $\alpha$ transfer channels were treated explicitly, using the real optical potentials and inelastic scattering form factors determined by the double-folding model. We show that a consistent CRC description of the elastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ data at different energies can be obtained over the whole angular region, using the $\alpha$ spectroscopic factors determined recently in the large scale SM calculation. The present CRC results are, therefore, of interest not only for the nuclear scattering studies but also provide an important spectroscopic information on the cluster dissociation of ${}^{16}\mathrm{O}$.

Figure 1

Kinematical illustration of the elastic scattering and elastic $\alpha$ transfer processes in the ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ system.

Figure 2

OM description of the elastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ data at $E_{\mathrm{lab}}=100$, 115.9, and 124 MeV [11] given by the best-fit real folded OP and WS imaginary OP (see parameters in Table 1). The far-side scattering cross sections are given by the near-far decomposition (2) using the same real folded OP but with different strengths $W_V$ of the WS imaginary OP (dashed and dotted lines). Ak is the $k\mathrm{th}$ order Airy minimum.

Figure 3

OM description of the elastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ data at $E_{\mathrm{lab}}=115.9$ MeV [11] given by the best-fit real folded OP and WS imaginary OP containing both the volume and surface terms (solid lines). The different behaviors of the near-side cross section at large angles are caused by two different values of the diffuseness $a_V$ of the volume WS term of the imaginary OP.

Figure 4

CRC description (solid lines) of the elastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ data measured at $E_{\mathrm{lab}}=100$ and 115.9 MeV [11]. The true elastic scattering cross section (dashed lines) is obtained with the real folded potential and WS imaginary potential taken from Table 1. The elastic $\alpha$ transfer cross section (dotted lines) is given by the best-fit $\alpha$ spectroscopic factor $S_{\alpha }\approx 1.96$.

Figure 5

The same as Fig. 4 but for the elastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ data measured at $E_{\mathrm{lab}}=132$ [9, 10], and 300 MeV [12].

Figure 6

Coupling scheme of the ten reaction channels taken into account in the present CRC analysis of the elastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ scattering that includes both the direct and indirect $\alpha$ transfer processes (see details in text).

Figure 7

Full CRC description of the elastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ scattering data measured at $E_{\mathrm{lab}}=100$ and 115.9 MeV [11] (solid lines) in comparison with the CC results for purely elastic scattering, neglecting the $\alpha$ transfer (dash-dotted lines), the CRC results including the (direct) two-channel $\alpha$ transfer (dotted lines), and the CRC results including the (direct and indirect via the $2_1^{+}$ state of the ${}^{12}\mathrm{C}$ core) four-channel $\alpha$ transfer (dashed lines). See more details in text.

Figure 8

The same as Fig. 7 but for the elastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ scattering data measured at $E_{\mathrm{lab}}=132$ MeV [9, 10], and 300 MeV [12].

Figure 9

Ten-channel CRC description (solid lines) of the elastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ data measured at $E_{\mathrm{lab}}=115.9$ and 124 MeV [11]. The total elastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ cross section is decomposed into the near-side (dotted lines) and far-side (dashed lines) contributions (2) using Fuller's method [36].

Figure 10

Explicit coupling between the true elastic scattering and nucleon transfer channels taken into account in the CRC calculation of the elastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ scattering. The $\alpha$-exchanged partition (b) of the ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ system cannot be populated by the nucleon transfer reaction.

Figure 11

CRC description of the elastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ scattering data measured at $E_{\mathrm{lab}}=115.9$ [11] and 300 MeV [12] based on the coupling scheme shown in Fig. 10. The solid lines are the results given by the full coupling between the true elastic scattering and all nucleon transfer channels. The CRC results obtained separately with the coupling to the neutron or proton transfer channel are shown as the dashed and dotted lines, respectively. The dash-dotted lines are the results of the OM calculation alone.

Figure 12

Two-way coupling between the true elastic scattering and sequential $\langle n,{}^3\mathrm{He}\rangle$ transfer channels taken into account in the CRC calculation of the elastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ scattering. The coupling scheme for the sequential $\langle p,{}^3\mathrm{H}\rangle$ transfer via the ${}^{15}\mathrm{N}+{}^{13}\mathrm{N}$ partitions at $-Q=10.18$ MeV is exactly the same.

Figure 13

CRC description of the elastic ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ scattering data measured at $E_{\mathrm{lab}}=115.9$ [11] and 300 MeV [12] based on the coupling scheme shown in Fig. 12. The solid lines are the results given by the full coupling between the true elastic scattering and sequential two-step $\langle n,{}^3\mathrm{He}\rangle$ and $\langle p,{}^3\mathrm{H}\rangle$ transfer channels. The CRC results obtained separately with the coupling to the $\langle n,{}^3\mathrm{He}\rangle$ or $\langle p,{}^3\mathrm{H}\rangle$ transfer channel are shown as the dashed and dotted lines, respectively. The dash-dotted lines are the results of the OM calculation alone.