Measurement of incomplete fusion cross sections in ${}^{6,7}\mathrm{Li}+{}^{238}\mathrm{U}$ reactions

Background: Incomplete fusion (ICF) in reactions involving weakly bound projectiles is understood to play an important role in enhancing the ratio of asymmetric to symmetric fission at $E\le V_b$, widening the fission fragment folding angle distribution at $E\le V_b$ and suppressing the complete fusion (CF) cross section at $E>V_b$. Experimental cross sections for individual ICF channels are necessary to obtain quantitative estimates of the above effects.

Purpose: Measurement of the cross sections for individual transfer-induced or ICF-fission channels in ${}^{6,7}\mathrm{Li}+{}^{238}\mathrm{U}$ reactions to explain quantitatively the difference in the ratio of asymmetric to symmetric fission for total fission and CF fission.

Methods: Triple coincidence measurement of two fission fragments and one light charged projectilelike fragment (PLF) is carried out using two multiwire proportional counter (MWPC) detectors and an array of CSI(Tl) scintillation detectors at energies near the Coulomb barrier. By calculating the efficiency of the detectors by Monte Carlo simulation and fission probability by GEF code, the angle-integrated ICF cross sections corresponding to p, d, t, and $\alpha$ emission are obtained. Mass distributions for total fission are calculated by adding the distributions for CF fission and all ICF fissions with weight factors proportional to the measured cross sections.

Results: ICF cross sections corresponding to $\alpha$ emission are found to be the highest in both the reactions. The relative contribution of ICF to total fusion at the lowest measured energy is found to be $\approx 70\%$ and it decreases with increasing projectile energy, consistent with the systematics of several reactions involving the same weakly bound projectiles. The simulated mass distributions for total fission are found to reproduce the experimental mass distributions.

Conclusions: Deuteron (triton) capture is observed to be the major ICF channel in the reaction involving ${}^6\mathrm{Li}\left({}^7\mathrm{Li}\right)$ projectile. The ratio of the sum of ICF to total fusion cross section for the present systems are consistent with the systematics. The difference in the ratio of asymmetric to symmetric fission between total fission and CF fission is explained quantitatively.

Figure 1

Schematic diagram of the experimental setup inside the scattering chamber consisting of two MWPC detectors (MWPC1 and MWPC2) to detect fission fragments, two transmission-type START detectors (S1 and S2), four CsI(Tl) detectors (C1–C4) ($4\times 4$ crystals) to detect light charged particles, and two monitor detectors (M1 and M2) kept at $\pm {10}^{\circ }$.

Figure 2

Typical spectra involving 40 MeV ${}^6\mathrm{Li}$ beam correspond to (a) 2D plot of the timings T1 versus T2 of the gas detectors MWPC1 and MWPC2, respectively, (b) 1D plot of the TAC between OR of MWPCs and OR of CsI(Tl) detectors, and (c) 2D plot of particle identification (PID) versus energy gated with the TAC and the banana gate on MWPC timings, shown in spectra (a).

Figure 3

The differential ICF cross sections at 40 MeV (red circle), 34 MeV (blue square), and 30 MeV (pink star) projectile energies corresponding to the ejectiles (a) $\alpha$, (b) triton, (c) deuteron, and (d) proton in ${}^6\mathrm{Li}+{}^{238}\mathrm{U}$ reaction. The fit to each of the data has been shown by dashed lines.

Figure 4

The differential ICF cross sections at 41.4 MeV (red circle) and 31.4 MeV (pink star) projectile energies corresponding to the ejectiles (a) $\alpha$, (b) triton, (c) deuteron, and (d) proton in ${}^7\mathrm{Li}+{}^{238}\mathrm{U}$ reaction. The fit to each of the data has been shown by dashed line.

Figure 5

The angle integrated ICF cross sections corresponding to the ejectile $\alpha$ (red circle), t (blue square), d (green diamond), and p (pink star) at different projectile energies for (a) ${}^6\mathrm{Li}$ and (b) ${}^7\mathrm{Li}$. Black triangles represent CF cross sections estimated from the relation “${\sigma }^{\mathrm{CF}}={\sigma }^{\mathrm{TF}}-{\mathrm{\Sigma }}_i{\sigma }_i^{\mathrm{ICF}}$”.

Figure 6

The ratios of total ICF cross section to total fusion cross section for the present systems ${}^6\mathrm{Li}+{}^{238}\mathrm{U}$ (red filled circles) and ${}^7\mathrm{Li}+{}^{238}\mathrm{U}$ (red hollow circles) have been compared with the literature data for ${}^7\mathrm{Li}+{}^{124}\mathrm{Sn}$ [25], ${}^6\mathrm{Li}+{}^{124}\mathrm{Sn}$ [38], ${}^6\mathrm{Li}+{}^{209}\mathrm{Bi}$ [24], and for ${}^7\mathrm{Li}+{}^{209}\mathrm{Bi}$ [24], ${}^7\mathrm{Li}+{}^{238}\mathrm{U}$ [31], ${}^7\mathrm{Li}+{}^{198}\mathrm{Pt}$ [30], and ${}^7\mathrm{Li}+{}^{159}\mathrm{Tb}$ [39].

Figure 7

A systematics of the total fusion (TF) cross sections for reactions involving several different targets such as ${}^{24}\mathrm{Mg}$ [40], ${}^{28}\mathrm{Si}$ [41, 42], ${}^{59}\mathrm{Co}$ [43], ${}^{64}\mathrm{Zn}$ [44], ${}^{124}\mathrm{Sn}$ [25, 38], ${}^{159}\mathrm{Tb}$ [25, 38], ${}^{197}\mathrm{Au}$ [45], and ${}^{232}\mathrm{Th}$ [35] along with the present target ${}^{238}\mathrm{U}$ (red filled circles) [35] with projectile (a) ${}^6\mathrm{Li}$ and (b) ${}^7\mathrm{Li}$, respectively.

Figure 8

A systematics of the ratio of total fusion (TF) cross sections for reactions involving ${}^6\mathrm{Li}$ to ${}^7\mathrm{Li}$ with several different targets like ${}^{24}\mathrm{Mg}$ [40], ${}^{28}\mathrm{Si}$ [41, 42], ${}^{59}\mathrm{Co}$ [43], ${}^{64}\mathrm{Zn}$ [44], ${}^{124}\mathrm{Sn}$ [25, 38], ${}^{159}\mathrm{Tb}$ [25, 38], ${}^{197}\mathrm{Au}$ [45]) and ${}^{232}\mathrm{Th}$ [35] along with the present target ${}^{238}\mathrm{U}$ (red filled circles) [35].

Figure 9

Mass distributions for CF fission and $\alpha$-, t-, d-, and p-gated fission have been shown by black dotted, red short-dashed, pink long-dashed, blue dash-dotted, and green dash-dot-dotted lines, respectively, for 30 MeV ${}^6\mathrm{Li}+{}^{238}\mathrm{U}$ system. The overlapping mass distributions obtained from Eq. (3) have been shown by solid red line.