Analysis of proton $+{}^{12}\mathrm{C}$ scattering by microscopic coupled-channels calculations

The microscopic coupled-channel (MCC) calculations for proton $+{}^{12}\mathrm{C}$ inelastic scattering are performed in the energy range of $E_p=29.95$ to 65 MeV. The nuclear interactions for the proton-${}^{12}\mathrm{C}$ system are constructed from the folding model, which employs the internal wave function of ${}^{12}\mathrm{C}$, obtained from the $3\alpha$ resonating group method ($3\alpha$ RGM), and an effective nucleon-nucleon interaction of the density-dependent Michigan three-range Yukawa (DDM3Y). The MCC calculation with the $3\alpha$ RGM + DDM3Y nicely reproduces all of the differential cross sections for elastic and inelastic scattering in the angular range of ${\theta }_{\mathrm{c}.\mathrm{m}.}=30$ to ${120}^{\circ }$. The channel-coupling effect is analyzed by comparing the full MCC calculation with the calculation of the distorted wave Born approximation (DWBA). The effect of the spin-orbit interaction, obtained in a simplified manner with the folding procedure, is also discussed.

Figure 1

Differential cross section of the elastic($0_1^{+}$) scattering in the range of $E_{\mathrm{lab}}=29.95$ to 65 MeV. The asterisks and the curves represent the experimental data and the theoretical calculations, respectively.

Figure 2

Same as Fig. 1 except for the inelastic $2_1^{+}$ channel.

Figure 3

Same as Fig. 1 except for the inelastic $3_1^{-}$ channel.

Figure 4

Same as Fig. 1 except for the inelastic $0_2^{+}$ channel.

Figure 5

Comparison of the full CC calculations with the DWBA calculations in the elastic channel. The solid curve shows the result of the full CC calculations, while the dashed curves represent the DWBA calculations.

Figure 6

Same as Fig. 5 except for the inelastic $2_1^{+}$ channel.

Figure 7

Same as Fig. 5 except for the inelastic $3_1^{-}$ channel.

Figure 8

Same as Fig. 5 except for the inelastic $0_2^{+}$ channel.

Figure 9

Comparison of the restricted CC calculation without $2_2^{+}$ and the DWBA calculations in the inelastic scattering to the $0_2^{+}$ channel. The solid curve represent the results of the restricted CC calculation without the channel coupling to the $2_2^{+}$ channel, while the DWBA results are plotted by the dashed curves. The DWBA results are the same as the dashed curves shown in the Fig. 8.

Figure 10

Differential cross section at $E_p=65\mathrm{MeV}$ in the $0_1^{+}$ and $0_2^{+}$ channels. The asterisk and curve represent the theoretical calculations, respectively.

Figure 11

The same as Fig. 10 except for the calculation with the modified treatment of the spin-orbit potentials. See text for details.

Figure 12

Distributions of the partial cross sections for the elastic at $E_p=65$ MeV. The asterisks show the results of the calculation with the full spin-orbit potential, while the solid squares represent the results with the restricted spin-orbit potential. See text for details.

Figure 13

The same as Fig. 12 except for the inelastic channels of the $0_2^{+}$ state.