Fusion hindrance for a positive $Q$-value system

An excitation function for the fusion reaction ${}^{28}\mathrm{Si}$ $+$ ${}^{30}\mathrm{Si}$ ($Q=14.3\mathrm{MeV}$) has been measured down to $40\mu b$. Deviations from the behavior predicted by the optical model and standard coupled-channels calculations have been observed in this system. The fusion cross sections can be reproduced by a shallow potential model well, which was originally developed to explain the hindrance of heavy-ion fusion for systems with negative $Q$-values.

Figure 1

Comparisons of experimental evaporation residue cross sections with various calculations for the system ${}^{28}\mathrm{Si}$ $+$ ${}^{30}\mathrm{Si}$. Green solid: optical model, black: CC with shallow potential. Light-blue dash-dotted: CC with Woods-Saxon potential. Magenta dotted: an extrapolation corresponding to the curve: $L(E)=A_0+B_0/E^{1.5}$ in Fig. 3a.

Figure 2

Comparison of potentials used in the CC calculations. For Ref. 17, different diffusenesses $a_{\mathrm{rep}}$ of the hard core density are used ($a_{\mathrm{rep}}=0.42,0.415,0.41$ fm, respectively). The black double-dotted curve is the pure M3Y potential.

Figure 3

(a) The logarithmic derivative $L(E)=d(\ln \sigma E)/\mathit{dE}$ plotted as a function of the center-of-mass energy $E$. The solid circles were derived from the data by least-squares fits to three consecutive data points while the open circles were obtained with the two-points method. The magenta dotted curve is a fit to the low energy part of the data with a formula $L(E)=A_0+B_0/E^{1.5}$. (b) The $S$ factor versus $E$ plot. The magenta dotted curve is an extrapolated one. See text for details.