Disintegration locations in ${}^7\mathrm{Li}\to {}^8\mathrm{Be}$ transfer-triggered breakup at near-barrier energies

Background: At above-barrier energies, complete fusion cross sections in collisions of light weakly bound nuclei with heavy target nuclei are suppressed when compared to well-bound nuclei. Breakup of the projectilelike nucleus was proposed to be the cause. In addition to direct breakup, breakup following transfer was shown to be substantial.

Purpose: We investigate breakup in reactions with ${}^7\mathrm{Li}$, triggered by sub-barrier proton pickup to unbound states in ${}^8\mathrm{Be}$, which subsequently separate into two $\alpha$ particles.

Method: Measurements of sub-barrier disintegration of ${}^7\mathrm{Li}$ on a ${}^{58}\mathrm{Ni}$ target were made using the Heavy Ion Accelerator Facility at the Australian National University. Combining the experimental results with classical simulations of post-breakup acceleration, we study the sensitivity of $\alpha -\alpha$ energy and angle correlations to the proximity of disintegration to the target (proton donor) nucleus.

Results: The simulations indicate that disintegration as the colliding nuclei approach each other leads to large angular separations ${\theta }_{12}$ of the $\alpha$ fragments. The detectors allow for a maximum opening angle of ${\theta }_{12}={132}^{\circ }$, such that the present experiment is largely insensitive to breakup occurring when the collision partners approach each other. The data are consistent with disintegration of (a) the $0^{+}{}^8\mathrm{Be}$ ground state far from the targetlike nucleus, and (b) the $2^{+}{}^8\mathrm{Be}$ resonance near the targetlike nucleus when the ${}^8\mathrm{Be}$ is receding from the targetlike nucleus.

Conclusions: The present results shed light on the near-target component of transfer-induced breakup reactions. The distribution of events with respect to the opening angle of the $\alpha$ particles, and the orientation of their relative velocity with respect to the velocity of their center of mass, gives insights into their proximity to the target at the moment of breakup. Further measurements with larger angular coverage and more complete simulations are required to fully understand the influence of breakup on fusion.

Figure 1

${}^7\mathrm{Li}$ projectile trajectories (solid and dotted lines) corresponding to a distance of closest approach $R_0$ (dashed arcs). Proton pickup occurs at some point on the solid trajectory to form ${}^8\mathrm{Be}$. Disintegration of ${}^8\mathrm{Be}$ into two $\alpha$ particles can occur either (a) approaching (incoming trajectory) or (b) receding from (outgoing trajectory) the targetlike nucleus. The radial distance relative to $R_0$ at which breakup occurs is denoted by $\mathrm{\Delta }r$. The asymptotic opening angle of the two fragments, following post-acceleration by the target, is ${\theta }_{12}$. Events resulting in large angular separations ${\theta }_{12}$ correspond to large relative energies of the $\alpha$ fragments.

Figure 2

Relative energy distribution for the two $\alpha$ fragments following proton-pickup-induced disintegration of ${}^7\mathrm{Li}$ interacting with (a) a ${}^{208}\mathrm{Pb}$ target at 29 MeV and (b) a ${}^{58}\mathrm{Ni}$ target at 13.1 MeV. At lower energies a prominent peak associated with the ${}^8\mathrm{Be}$ ground state is seen highlighted by the shaded region. In both cases a second bump is seen at larger $E_{\mathrm{rel}}$, before the distribution decays exponentially.

Figure 3

The distribution of coincidence events according to their relative energy $E_{\mathrm{rel}}$ and difference of energies of the fragments $|E_1-E_2|$. The dashed arc shows the expected maximum difference, which should be attained for all $E_{\mathrm{rel}}$ in the absence of the target nucleus. The hatched area shows the detection limit assuming a threshold $\alpha$ energy of 1.75 MeV. Both estimates assume a constant total energy $E_1+E_2=14$ MeV.

Figure 4

Notation for fragment velocities for isolated disintegration. The laboratory frame opening angle is ${\theta }_{12}$. The orientation of the relative velocity with respect to that of the center of mass is $\beta$.

Figure 5

Plot of $\beta$ against ${\theta }_{12}$ showing the present measurements. The lines indicate the expected correlation for asymptotic breakup for an initial relative energy of 0.092 MeV (dashed) and 3.122 MeV (solid). The hatched area shows the expected ${\theta }_{12}$ inaccessible with the current detector configuration. In reality, the efficiency will decrease as this region is approached. The inset shows the projection of the 0.092-keV band onto $\beta$, with the red line showing the expected $sin\beta$ isotropic distribution. See text for further discussion.

Figure 6

Summary of model calculations and their comparison with data for the correlation between $\beta$ and ${\theta }_{12}$. (a) Curves for breakup distances near the distance of closest approach, where a negative value of $\mathrm{\Delta }r$ indicates breakup prior to $R_0$ and a positive value after. (b) Curves for fixed breakup distances $\mathrm{\Delta }r$ after the distance of closest approach. (c) Illustration of the sensitivity to the excitation energy (initial relative energy) of the fragments, covering the range of $E_R-\mathrm{\Gamma }/2$ to $E_R+\mathrm{\Gamma }/2$ for the $2^{+}$ resonance. (d) Illustration of the sensitivity to projectile-target angular momenta, represented by the points. The calculations for (c) and (d) were made with fixed $\mathrm{\Delta }r=8$ fm. See text for further discussion.

Figure 7

The distribution of events according to their relative energy $E_{\mathrm{rel}}$ and difference of energies $|E_1-E_2|$. A fixed excitation energy of 3.122 MeV was used and projectile-target angular momentum $L=0$. The dashed black arc again shows the maximal allowed $|E_1-E_2|$.