Relation between transition density and proton inelastic scattering by ${}^{12}\mathrm{C}$ target at $E_p=65$ and 200 MeV

We calculate proton elastic and inelastic scatterings with a microscopic coupled channel (MCC) calculation. The localized diagonal and coupling potentials including the spin-orbit part are obtained by folding a complex $G$-matrix effective nucleon-nucleon interaction with a transition density. This is the first time that the present folding prescription for the spin-orbit part is applied to the proton inelastic scattering, while for the monopole transition only. We apply the MCC calculation to the proton elastic and inelastic $\left(0_2^{+}\right)$ scatterings by ${}^{12}\mathrm{C}$ target at $E_p=65 \mathrm{and} 200 \mathrm{MeV}$. The role of diagonal and coupling potentials for the central and spin-orbit parts is checked. In addition, the relation between the transition density and the proton inelastic scattering is investigated with the modified wave function and the modified transition density. Namely, we perform the investigation with the artificial drastic change rather than fine structural change. The inelastic cross section is sensitive to the strength and shape of the transition density, but the inelastic analyzing power is sensitive only to the shape of that. Finally, we make clear the property of the inelastic analyzing power derived from the transition density without an ambiguity.

Figure 1

(a) Elastic and inelastic cross sections, (b) elastic analyzing powers, and (c) inelastic ($0_2^{+}$) analyzing powers of $p+{}^{12}\mathrm{C}$ system at 65 MeV. The solid curves are the results by the present MCC calculation. The experimental data are taken from Refs. [49, 50].

Figure 2

Same as Fig. 1 but at 200 MeV. The experimental data are taken from Refs. [49, 51, 52].

Figure 3

(a) Inelastic cross sections and (b) inelastic analyzing powers of $p+{}^{12}\mathrm{C}$ system at 65 MeV. The solid curves are same results shown in Figs. 1 and 2. The dotted curves show the results without the diagonal potential of the elastic channel (gs) for the central part. The dashed curves are obtained without the coupling potential between ground state and excited state ($0_2^{+}$) for the central part. The dot-dashed curves show the results without the diagonal potential of the excited channel ($0_2^{+}$) (ex) for the central part.

Figure 4

Same as described in the caption of Fig. 3 but for the spin-orbit (LS) part.

Figure 5

Same as described in the caption of Fig. 3 but at 200 MeV.

Figure 6

Same as described in the caption of Fig. 4 but at 200 MeV.

Figure 7

Transition densities obtained by modified ACM wave functions. The meaning of the curves is introduced in the text.

Figure 8

(a) Inelastic cross sections and (b) inelastic analyzing powers of $p+{}^{12}\mathrm{C}$ system at 65 MeV with the transition densities obtained by the modified ACM wave function.

Figure 9

Same as described in the caption of Fig. 8 but at 200 MeV.

Figure 10

Modified transition densities. The detail is introduced in the text.

Figure 11

Same as described in the caption of Fig. 8 but with the transition densities as shown in Fig. 10.

Figure 12

Same as described in the caption of Fig. 11 but at 200 MeV.