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

TL;DR

This study uses a microscopic coupled channel approach to analyze proton inelastic scattering on $^{12}$C at 65 and 200 MeV, revealing the relationship between transition density and scattering observables, especially the analyzing power.

Contribution

First application of a folding prescription for the spin-orbit potential to proton inelastic scattering, exploring the sensitivity of scattering observables to transition density modifications.

Findings

Inelastic cross sections are sensitive to transition density strength and shape.

Inelastic analyzing power depends only on the shape of the transition density.

The property of analyzing power can be derived from transition density without ambiguity.

Abstract

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 (0$^+_2$) scatterings by $^{12}$C target at $E_p$ = 65 and 200 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.