Study of elastic and inelastic scattering of $^7$Be + $^{12}$C at 35 MeV

TL;DR

This study investigates elastic and inelastic scattering of $^7$Be on $^{12}$C at 35 MeV, including first measurements of inelastic scattering to the 4.439 MeV state, using optical and coupled-channel models to analyze the data.

Contribution

First measurement of inelastic scattering to the 4.439 MeV state of $^{12}$C at this energy, with comprehensive optical and coupled-channel analysis including breakup effects.

Findings

Breakup channel coupling affects elastic scattering.

Inelastic excitation of $^{12}$C is significant, mutual excitation is smaller.

Reaction cross section aligns with Wong's calculations.

Abstract

The elastic and inelastic scattering of $^7$Be from $^{12}$C have been measured at an incident energy of 35 MeV. The inelastic scattering leading to the 4.439 MeV excited state of $^{12}$C has been measured for the first time. The experimental data cover an angular range of $\theta_{cm}$ = 15$^{\circ}$-120$^{\circ}$. Optical model analyses were carried out with Woods-Saxon and double-folding potential using the density dependent M3Y (DDM3Y) effective interaction. The microscopic analysis of the elastic data indicates breakup channel coupling effect. A coupled-channel analysis of the inelastic scattering, based on collective form factors, show that mutual excitation of both $^7$Be and $^{12}$C is significantly smaller than the single excitation of $^{12}$C. The larger deformation length obtained from the DWBA analysis could be explained by including the excitation of $^7$Be in a coupled-channel analysis. The breakup cross section of $^7$Be is estimated to be less than 10$\%$ of the reaction cross section. The intrinsic deformation length obtained for the $^{12}$C$^*$ (4.439 MeV) state is $\delta _2$ = 1.37 fm. The total reaction cross section deduced from the analysis agrees very well with Wong's calculations for similar weakly bound light nuclei on $^{12}$C target.