Folding model analysis of 240 MeV ${}^6\mathrm{Li}$ elastic scattering on ${}^{116}\mathrm{Sn}$ and inelastic scattering to low-lying states of ${}^{116}\mathrm{Sn}$

Elastic scattering of 240 MeV ${}^6\mathrm{Li}$ ions from ${}^{116}\mathrm{Sn}$ was measured from $4^{°}⩽{\theta }_{\mathrm{c}.\mathrm{m}.}⩽{32}^{°}$. The data were fitted with a Woods-Saxon phenomenological potential and with double folding models using the $M3Y$ $\mathit{NN}$ effective interaction with and without density dependence. DWBA calculations with the fitted parameters were used to calculate cross sections for inelastic scattering to low-lying $2^{+}$and $3^{-}$ states. $B(E2)$ and $B(E3)$ values were extracted and compared with electromagnetic values and those obtained from $\alpha$ inelastic scattering.

Figure 1

Experimental angular distribution of the cross section (relative to Rutherford cross section) and fits for ${}^6\mathrm{Li}$${+}^{116}$Sn elastic scattering using WS potential, DIF potential and DDF potential parameters are shown. The error bars indicate statistical and systematic errors.

Figure 2

Real optical potentials obtained from WS, DIF, DDF models. For DIF model, the dash and dot curve shows the folded potential obtained from CHEN2 multiplied by renormalization factor $N_R=0.637$. For DDF model, the black curve shows the folded potential obtained from DFPD4 multiplied by renormalization factor $N_R=0.659$. The inset has the vertical scale expanded to show the region of overlap.

Figure 3

The volume integral for real part of optical potential obtained with WS model, DIF model and DDF model. The curves with dash, black, dash and dot represent Nadasen et al.'s expression obtained with WS potential [16], Gupta and Murthy's expression obtained with $\mathrm{JLM}$ effective interaction [40] and Satchler's expression obtained with S1Y effective $\mathit{NN}$ interaction [27], respectively. Volume integrals obtained from Ref. [8] for 210 MeV ${}^6\mathrm{Li}$ scattering on ${}^{90}\mathrm{Zr}$ are also plotted in the figure for comparison.

Figure 4

The differential cross-sections calculated with deformed potential model and folding models for inelastic scattering to the 1.29 MeV $2^{+}$state of ${}^{116}\mathrm{Sn}$ along with the data points are plotted versus average center of mass angle. The $B(E2)$ values used for DP, DIF, and DDF models calculations are best fit values of $0.229,0.182,0.233e^2{b}^2$respectively. The error bars represent statistical and systematic errors.

Figure 5

The differential cross-sections calculated with deformed potential model and folding models for inelastic scattering to the 2.27 MeV $3^{-}$state of ${}^{116}\mathrm{Sn}$ along with the data points are plotted versus average center of mass angle. The $B(E3)$ value used for DP, DIF, and DDF models calculations are best fit values of $0.116,0.101,0.133e^2{b}^3$respectively. The error bars represent statistical and systematic errors.