Probing the fusion of neutron-rich nuclei with re-accelerated radioactive beams

We report the first measurement of the fusion excitation functions for ${}^{39,47}\mathrm{K}+{}^{28}\mathrm{Si}$ at near-barrier energies. Evaporation residues resulting from the fusion process were identified by direct measurement of their energy and time of flight with high geometric efficiency. At the lowest incident energy, the cross section measured for the neutron-rich ${}^{47}\mathrm{K}$-induced reaction is $\approx 6$ times larger than that of the $\beta$-stable system. This experimental approach, both in measurement and in analysis, demonstrates how to efficiently measure fusion with low-intensity re-accelerated radioactive beams, establishing the framework for future studies.

Figure 1

Schematic of the experimental setup. See the text for details.

Figure 2

Energy versus mass number for reaction products with $2.4^{\circ }\le {\theta }_{\mathrm{lab}}\le 7.3^{\circ }$. For reference, a solid (black) line and a dashed (red) line are shown at $A=47$ and $A=36$, respectively. Evaporation residues are shown in bold. The inset: Mass distribution of evaporation residues.

Figure 3

Experimental fusion excitation functions for ${}^{39,47}\mathrm{K}+{}^{28}\mathrm{Si}$. The open and closed symbols depict the results for the ${}^{39}\mathrm{K}$ and ${}^{47}\mathrm{K}$ beams, respectively. The dashed and solid lines correspond to a fit of the experimental data with the Wong parametrization [25].

Figure 4

Panel (a) Experimental data for ${}^{47}\mathrm{K}+{}^{28}\mathrm{Si}$ are represented by symbols. The dashed (colored) lines correspond to different models described in the text. Panel (b): The same as above for ${}^{39}\mathrm{K}$ projectile ions. Panel (c) The relative cross-section $\sigma \left({}^{47}\mathrm{K}\right)/\sigma \left({}^{39}\mathrm{K}\right)$ is depicted as a solid (black) line, corresponding to the ratio of the Wong [25] fits of the experimental data. The shaded band represents the measurement uncertainty. The dashed (colored) lines correspond to model calculations described in the text.