Projectile-breakup-induced fission-fragment angular distributions in the ${}^6\mathrm{Li}+{}^{232}\mathrm{Th}$ reaction

Background: Experimental anisotropy in fission-fragment (FF) angular distribution in reactions involving weakly bound stable projectiles with actinide targets are enhanced compared to statistical saddle-point model (SSPM) predictions. Contributions from breakup- or transfer-induced fission to total fission are cited as possible reasons for such enhancement.

Purpose: To identify the breakup- or transfer-induced fission channels in ${}^6\mathrm{Li}$+${}^{232}\mathrm{Th}$ reaction and to investigate their effects on FF angular anisotropy.

Methods: The FF angular distributions have been measured exclusively at three beam energies (28, 32, and 36 MeV) around the Coulomb barrier in coincidence with projectile breakup fragments like $\alpha , d$, and $p$ using Si strip detectors. The angular anisotropy obtained for different exclusive breakup- or transfer-induced fission channels are compared with that for total fission. SSPM and pre-equilibrium fission models have been employed to obtain theoretical FF angular anisotropy.

Results: Angular anisotropy of the fission fragments produced by different transfer- or breakup-induced fission reactions have been obtained separately in the rest frame of respective recoiling nuclei. Some of these anisotropies were found to be stronger than those of the inclusive fission. Overall angular distributions of transfer or breakup fission, integrated over all possible recoil angles with weight factor proportional to differential cross section of the complementary breakup fragment emitted in coincidence in all possible directions, were obtained. It was observed that the overall FF angular anisotropy for each of these fission channels is less than or equal to the anisotropy of total fission at all the measured energies. Assuming isotropic out-of-plane correlations between the fission fragments and light-charged particles, the overall breakup- or transfer-induced fission fragment angular distributions do not explain the observed enhancement in FF anisotropy of total fission. Pre-equilibrium fission model provides a reasonable explanation of the enhanced experimental anisotropy of total fission.

Conclusions: Angular anisotropies for different breakup or transfer fission channels involving emission of $\alpha , d$, and $p$ in the reaction plane have been measured for the ${}^6\mathrm{Li}+{}^{232}\mathrm{Th}$ reaction. The overall FF angular anisotropies of breakup- or transfer-induced fissions do not explain the enhanced anisotropy of total fission at near-barrier energies. A measurement of out-of-plane correlation is necessary to confirm the above observation and obtain a complete picture on the effect of transfer or breakup on total fission.

Figure 1

Schematic diagram of the experimental setup inside scattering chamber with four single silicon strip detectors ($F_1–F_4$) to detect fission fragments, three telescopes ($T_1–T_3$) made of $\mathrm{\Delta }E-E$ silicon strip detectors to detect light charged particles, and two monitor detectors ($M_1$ and $M_2$).

Figure 2

(a) Typical spectrum of fission fragments detected in one of the 16 strips of $F_3$ fission detector in coincidence with the projectile-like fragments in any of the three telescopes ($T_1$ or $T_2$ or $T_3$) at $E_{\mathrm{beam}}=36$ MeV, (b) typical two-dimensional ($\mathrm{\Delta }E-E$) raw spectrum for light charged particles ($Z=1–3$) detected by $T_3$ telescope in coincidence with fission fragments in any of the four fission detectors ($F_1$ or $F_2$ or $F_3$ or $F_4$), and (c) one-dimensional projection of $\alpha$ band, selected from the above two-dimensional plot, on the $x$ axis.

Figure 3

Inclusive (total) fission fragment angular distribution at beam energies of (a) 28, (b) 32, and (c) 36 MeV.

Figure 4

Fission-fragment angular anisotropy for inclusive fission obtained from the present data (filled circle) and the existing data by Freiesleben et al. [15] (hollow circle) are compared with SSPM calculations (solid line) at near-barrier energies.

Figure 5

Angular distributions of $\alpha$-gated fission fragments in the rest frame of the recoil nuclei for the beam energies of (a) 32 MeV and (b) 36 MeV when $\alpha$ is detected in the forward angles.

Figure 6

Angular distributions of $\alpha$-gated fission fragments in the rest frame of the recoil nuclei for the beam energies of (a) 28 MeV, (b) 32 MeV, and (c) 36 MeV when $\alpha$ is detected at the backward angles.

Figure 7

Angular distribution for fission fragments measured in $F_1–F_4$ detectors in coincidence with deuterons detected by the telescopes in the angular range of (a) $158–{166}^{\circ }$ for $E_{\mathrm{beam}}=32$ MeV and (b) $76–{84}^{\circ }$ for $E_{\mathrm{beam}}=36$ MeV.

Figure 8

Angular distribution for fission fragments measured in $F_1–F_4$ detectors in coincidence with protons detected by the telescopes in the angular range of (a) $158–{166}^{\circ }$ for $E_{\mathrm{beam}}=32$ MeV and (b) $76–{84}^{\circ }$ for $E_{\mathrm{beam}}=36$ MeV.

Figure 9

Differential cross sections for (a) inclusive $\alpha$ at $E_{\mathrm{beam}}=28$, 32, and 36 MeV, (b) inclusive deuteron at $E_{\mathrm{beam}}=32$ and 36 MeV, and (c) inclusive proton at $E_{\mathrm{beam}}=32$ and 36 MeV, produced in the ${}^6\mathrm{Li}+{}^{232}\mathrm{Th}$ reaction.

Figure 10

Estimated overall angular distributions of breakup- or transfer-induced fission fragments in coincidence with $p, d$, and $\alpha$ emitted in all possible directions, with respect to the beam axis in the center-of-mass frame.

Figure 11

Fission-fragment angular anisotropy for total fission obtained from present data (filled circle) are compared with the calculations using ECD $K$-state model (solid line) at near-barrier energies.

Figure 12

Schematic diagram showing the angles of fission-fragment emission ${\theta }_{\mathrm{fission}}$ and recoils ${\theta }_{\mathrm{recoil}}$. The dotted blue line represents possible out-of-plane recoil angles and ${\theta }^{\prime }$ is the angle between the recoil direction and one of the fission fragments.