Fusion Suppression and Sub-Barrier Breakup of Weakly Bound Nuclei

The mechanism for the large suppression of complete fusion in the ${}^{\mathrm{9}}\mathrm{B}\mathrm{e}+{}^{\mathrm{208}}\mathrm{P}\mathrm{b}$ reaction has been investigated through measurement of sub-barrier breakup of ${}^{\mathrm{9}}\mathrm{B}\mathrm{e}$. Excluding breakup through the ${}^{\mathrm{8}}\mathrm{B}\mathrm{e}$ ground state, whose lifetime is too long, a prompt breakup component remains, having sufficient probability to explain the observed suppression of complete fusion. This appears to be associated with interactions at the nuclear surface. The fusion suppression is predicted to be almost proportional to the charge of the target nucleus, making it most significant in reactions with heavy nuclei.

Figure 1

Energy spectra of singles $\alpha$ particles (left panels) and corresponding $\alpha$ doubles (right), observed at $166°$, for the indicated beam energies incident on the ${}^{\mathrm{n}\mathrm{a}\mathrm{t}}\mathrm{P}\mathrm{b}$ target. The predicted singles spectra resulting from the observed doubles events, assuming ${}^{\mathrm{8}}\mathrm{B}\mathrm{e}$ g.s. decay, are shown by the thick line histograms in the left panels, and the spectrum after subtraction of this component is labeled ${}^{\mathrm{8}}\mathrm{B}\mathrm{e}$ g.s. subtracted.

Figure 2

The estimated total breakup cross sections from this work are shown by the filled points. The measured cross sections for complete and incomplete fusion, and the calculated fusion without breakup, are from Ref. 3. The arrow marks the measured average fusion barrier energy.

Figure 3

Ratio of measured to Rutherford differential cross sections as a function of the distance of closest approach on a Coulomb trajectory $R_{\mathrm{m}\mathrm{i}\mathrm{n}}$, for each process. The full lines are exponential fits to the experimental data. The grey diamonds represent the calculated yield for Coulomb excitation to the first two excited states of ${}^{\mathrm{9}}\mathrm{B}\mathrm{e}$, scaled up by a factor of 2 (see text). The dashed line shows the calculated slope for $E2$ Coulomb excitation.