Influence of Nuclear Structure on Sub-Barrier Hindrance in $\mathrm{N}\mathrm{i}+\mathrm{N}\mathrm{i}$ Fusion

Fusion-evaporation cross sections for ${}^{64}\mathrm{N}\mathrm{i}+{}^{64}\mathrm{N}\mathrm{i}$ have been measured down to the 10 nb level. For fusion between two open-shell nuclei, this is the first observation of a maximum in the $S$-factor, which signals a strong sub-barrier hindrance. A comparison with the ${}^{58}\mathrm{N}\mathrm{i}+{}^{58}\mathrm{N}\mathrm{i}$, ${}^{58}\mathrm{N}\mathrm{i}+{}^{60}\mathrm{N}\mathrm{i}$, and ${}^{58}\mathrm{N}\mathrm{i}+{}^{64}\mathrm{N}\mathrm{i}$ systems indicates a strong dependence of the energy where the hindrance occurs on the stiffness of the interacting nuclei.

Figure 1

Experimental evaporation residue cross sections $\sigma \left(E\right)$ (solid circles) plotted as a function of laboratory energy $E_{\mathrm{l}\mathrm{a}\mathrm{b}}$ for the system ${}^{64}\mathrm{N}\mathrm{i}+{}^{64}\mathrm{N}\mathrm{i}$. The incident energies have been corrected for the finite target thickness. The uncertainties in the cross sections for many points are smaller than the size of the symbol. Previous measurements from Refs. 7, 8 are shown as solid and open triangles, respectively. The dashed and solid curves represent coupled-channels calculations, which are fit to the high energy part of the present data (see text for details).

Figure 2

(a) The logarithmic derivative $L\left(E\right)=d(\ln \sigma E)/dE$ plotted as a function of center-of-mass energy $E$. The solid circles were derived from the data by least-squares fits to three consecutive data points. Coupled-channels calculations are shown as the solid and dotted curves, whereas the dash-dotted curve corresponds to a constant $S$ factor. (b) The $S$ factor for ${}^{64}\mathrm{N}\mathrm{i}+{}^{64}\mathrm{N}\mathrm{i}$ (solid points) is compared to that for ${}^{58}\mathrm{N}\mathrm{i}+{}^{58}\mathrm{N}\mathrm{i}$ [4] (open points). The solid curve represents a coupled-channels calculation using $a_i=5\mathrm{f}\mathrm{m}$ for the ${}^{64}\mathrm{N}\mathrm{i}+{}^{64}\mathrm{N}\mathrm{i}$ system. The dotted curve is a coupled-channels calculation taken from Ref. 14. The parameter ${\eta }_0$ used to bring different fusion systems onto the same scale are ${\eta }_0=75.23$ and ${\eta }_0=69.99$ for the ${}^{64}\mathrm{N}\mathrm{i}+{}^{64}\mathrm{N}\mathrm{i}$ and ${}^{58}\mathrm{N}\mathrm{i}+{}^{58}\mathrm{N}\mathrm{i}$ systems, respectively.

Figure 3

Systematics of the energy $E_s$, where the $S$ factor has a maximum as a function of the parameter, $Z_1{Z}_2\sqrt{\mu }$. The solid curve represents the empirical expression given by Eq. (1). Solid circles were obtained for systems that exhibit a clear maximum in the $S$ factor, i.e., so-called category I systems [6]. Solid triangles were obtained by extrapolating the logarithmic derivative to the value for a constant $S$ factor (category II systems). Open circles show the lowest measured energy, $E_{\mathrm{m}\mathrm{i}\mathrm{n}}$, for those systems where no sign of a maximum in the $S$ factor has been found so far (category III systems). The inset gives an expanded view of the results for $\mathrm{N}\mathrm{i}+\mathrm{N}\mathrm{i}$ reactions.