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

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 12C has been measured for the first time. The experimental data cover an angular range of $\theta_{cm} = 15 \degree -120 \degree$. 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, shows 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 7Be 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.