Sub-barrier enhancement of fusion as compared to a microscopic method in ${}^{18}\mathrm{O}+{}^{12}\mathrm{C}$

Background: Measurement of the energy dependence of the fusion cross section at sub-barrier energies provides an important test for theoretical models of fusion.

Purpose: The aim of the study is to extend the measurement of fusion cross sections in the sub-barrier domain for the ${}^{18}\mathrm{O}+{}^{12}\mathrm{C}$ system, and to use the new experimental data to confront microscopic calculations of fusion.

Method: Evaporation residues produced in fusion of ${}^{18}\mathrm{O}$ ions with ${}^{12}\mathrm{C}$ target nuclei were detected with good geometric efficiency and identified by measuring their energy and time-of-flight. Theoretical calculations with a density-constrained time-dependent Hartree-Fock (DC-TDHF) theory include for the first time the effect of pairing on the fusion cross section.

Results: Comparison of the measured fusion excitation function with the predictions of the DC-TDHF calculations reveal that the experimental data exhibit a smaller decrease in cross section with decreasing energy than is theoretically predicted.

Conclusion: The larger cross sections observed at the lowest energies measured indicate a larger tunneling probability for the fusion process. This larger probability can be associated with a smaller, narrower fusion barrier than presently included in the theoretical calculations.

Figure 1

(a) Schematic illustration of the experimental setup. (b) Energy vs TOF spectrum for ${}^{18}\mathrm{O}$ ions incident on ${}^{12}\mathrm{C}$ target nuclei at $E_{\mathrm{c}.\mathrm{m}.}=14.4$ MeV. Color is used to represent yield in the two-dimensional spectrum on a logarithmic scale.

Figure 2

The fusion excitation function for ${}^{18}\mathrm{O}+{}^{12}\mathrm{C}$ is shown at energies near and below the Coulomb barrier. Literature values are shown as open circles [21], open squares [23], and open stars [22] with the present data represented by solid circles.

Figure 3

(a) Comparison of the experimentally measured fusion cross sections (closed symbols) with the results of the DC-TDHF calculations with (solid line) and without (dashed line) pairing. The results of coupled-channel calculations (ccfull) are indicated by the dot-dash line. Also shown, as a dotted line, is the result of a fit to the experimental data (see text for details). (b) Energy dependence of the ratio of the experimentally measured cross sections to the DC-TDHF predictions which include pairing. The shaded band depicts the uncertainty in the ratio due to the uncertainty in the experimental cross sections.