Unexpected Behavior of Heavy-Ion Fusion Cross Sections at Extreme Sub-Barrier Energies

The excitation function for fusion evaporation in the ${\text{\hspace{0.17em}︀}}^{60}\text{Ni}+{\text{\hspace{0.17em}︀}}^{89}\text{Y}$ system was measured over a range in cross section covering 6 orders of magnitude. The cross section exhibits an abrupt decrease at extreme sub-barrier energies. This behavior, which is also present in a few other systems found in the literature, cannot be reproduced with present models, including those based on a coupled-channels approach. Possible causes are discussed, including a dependence on the intrinsic structure of the participants.

Figure 1

(a) Plots of $\sigma E$ versus $E/V_b$ for the systems ${\text{\hspace{0.17em}︀}}^{58}\mathrm{N}\mathrm{i}+{\text{\hspace{0.17em}︀}}^{58}\mathrm{N}\mathrm{i}$ and ${\text{\hspace{0.17em}︀}}^{90}\mathrm{Z}\mathrm{r}+{\text{\hspace{0.17em}︀}}^{\mathrm{92}}\mathrm{Z}\mathrm{r}$. The lines are the results of either coupled-channels calculations (solid) or a pheno­menological description with the Wong formula (dashed). See text for details. (b) ${\sigma }_{\mathrm{e}\mathrm{x}\mathrm{p}}/{\sigma }_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o}}$ vs $E/V_b$: circles: ${\sigma }_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o}}$ calculated using the Wong formula; crosses: ${\sigma }_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o}}$ calculated within the coupled-channels formalism.

Figure 2

Experimental evaporation residue cross sections $\sigma \left(E\right)$, (a) and ${\sigma }_{\mathrm{e}\mathrm{x}\mathrm{p}}/{\sigma }_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o}}$, (b) (${\sigma }_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o}}$ calculated from the Wong formula), plotted as a function of the center-of-mass energy for the system ${\text{\hspace{0.17em}︀}}^{60}\mathrm{N}\mathrm{i}+{\text{\hspace{0.17em}︀}}^{\mathrm{89}}\mathrm{Y}$. The incident energies have been corrected for the finite target thickness (including the influence of sharp changes in the excitation function with energy). The uncertainties in the cross sections are smaller than the points. Only an upper limit to the cross section was obtained at the lowest energy. The inset presents $M/Q$ spectra obtained at three center-of-mass energies.

Figure 3

Exponential slopes $L\left(E\right)$, $d\mathbf{\left[}\ln \right(\sigma E\left)\mathbf{\right]}/dE$, plotted as a function of $E/E_0$ for the systems ${\text{\hspace{0.17em}︀}}^{58}\mathrm{N}\mathrm{i}+{\text{\hspace{0.17em}︀}}^{58}\mathrm{N}\mathrm{i}$, ${\text{\hspace{0.17em}︀}}^{60}\mathrm{N}\mathrm{i}+{\text{\hspace{0.17em}︀}}^{\mathrm{89}}\mathrm{Y}$, and ${\text{\hspace{0.17em}︀}}^{90}\mathrm{Z}\mathrm{r}+{\text{\hspace{0.17em}︀}}^{92}\mathrm{Z}\mathrm{r}$. Solid circles and stars correspond to slope determinations from consecutive data points and from least-squares fits to three data points, respectively. Solid and dashed lines are the results of theoretical calculations with the Wong formula and the coupled-channel formalism, respectively.