Origins of Incomplete Fusion Products and the Suppression of Complete Fusion in Reactions of ${}^7\mathrm{Li}$

Above-barrier complete fusion involving nuclides with low binding energy is typically suppressed by 30%. The mechanism that causes this suppression, and produces the associated incomplete fusion products, is controversial. We have developed a new experimental approach to investigate the mechanisms that produce incomplete fusion products, combining singles and coincidence measurements of light fragments and heavy residues in ${}^7\mathrm{Li}+{}^{209}\mathrm{Bi}$ reactions. For polonium isotopes, the dominant incomplete fusion product, only a small fraction can be explained by projectile breakup followed by capture: the dominant mechanism is triton cluster transfer. Suppression of complete fusion is therefore primarily a consequence of clustering in weakly bound nuclei rather than their breakup prior to reaching the fusion barrier. This implies that suppression of complete fusion will occur in reactions of nuclides where strong clustering is present.

Figure 1

Double differential cross sections $d^2\sigma /dEd\mathrm{\Omega }(E_{\alpha },{\theta }_{lab})$ for (a) $\alpha$ particles arising from no-capture breakup (NCBU) and (b) unaccompanied $\alpha$ particles in the reaction of ${}^7\mathrm{Li}$ with ${}^{209}\mathrm{Bi}$ at $E_{\mathrm{c}.\mathrm{m}.}=38.72\mathrm{MeV}$ ($E_{\mathrm{c}.\mathrm{m}.}/V_b=1.31$). The angular distributions are continuous across the 5° gap between the detectors, because the 4° angular bin boundary was in the middle of the gap. A diagonal cut at low energy and angle has been applied in panel (b) to remove the known contribution of light impurities. The $\alpha$ detected in coincidence with ${}^{212}\mathrm{Po}$ decays are indicated (event-by-event) by the dots in panels (a) and (b). Events below $\sim 38\mathrm{MeV}$ (shown in grey) cannot be genuine: the corresponding excitation energy of ${}^{212}\mathrm{Po}$ lies above its one-neutron separation energy $S_n=6.01\mathrm{MeV}$. They are interpreted to be random coincidences. Model calculations (described in text) of the double-differential cross sections for no-capture breakup $\alpha$ at the same energy are shown in panel (c). All panels have the same cross-section color scale. Panel (d) shows the differential cross sections $d\sigma /d\mathrm{\Omega }({\theta }_{\text{lab}})$ for unaccompanied $\alpha$ (orange points) and no-capture breakup $\alpha$ (blue points), compared to the model predictions of breakup capture (BUC) (orange curve) and from no-capture breakup (blue curve).

Figure 2

$Q$ value (bottom axis) and excitation energy $E_x$ of ${}^{212}\mathrm{Po}$ (top axis) distribution for unaccompanied $\alpha$ particles (orange) and $\alpha$ in coincidence with ${}^{212}\mathrm{Po}$ $\alpha$ decay (purple) produced in reactions of ${}^7\mathrm{Li}+{}^{209}\mathrm{Bi}$ at $E_{\mathrm{c}.\mathrm{m}.}=38.72\mathrm{MeV}$. The points have been multiplied by a factor of 100 for $Q>-5\mathrm{MeV}$ to show the events in coincidence with ${}^{212}\mathrm{Po}$ $\alpha$ decay. The one neutron separation energy of $S_n=6.01\mathrm{MeV}$ for ${}^{212}\mathrm{Po}$ is indicated by the arrow.

Figure 3

Predicted (shaded curves) cross sections for various polonium isotopes from the measured unaccompanied $\alpha$-excitation energy distribution folded with PACE4 calculations, compared to measured isotopic polonium cross sections (filled symbols) from $\alpha$ decay measurements [3]. The total unaccompanied $\alpha$ cross sections measured in the current work are indicated by the orange stars. The numbers along the band for ${}^{209}\mathrm{Po}$ show the predicted values of the cross sections at the points indicated by the crosses.