Fission fragment angular distributions in ${}^{6,7}\mathrm{Li}$ $+{}^{235,238}\mathrm{U}$ reactions

Fission fragment (FF) angular distributions for ${}^{6,7}\mathrm{Li}+{}^{235,238}\mathrm{U}$ reactions have been measured at energies near and above the Coulomb barrier. The angle integrated fission cross sections for ${}^6\mathrm{Li}$ induced reactions at sub-barrier energies are found to be higher than ${}^7\mathrm{Li}$ induced reactions possibly due to a larger contribution of breakup or transfer induced fission in cases of the former compared to the latter. The FF anisotropies for ${}^{6,7}\mathrm{Li}+{}^{235}\mathrm{U}$ are found to be slightly smaller than ${}^{6,7}\mathrm{Li}+{}^{238}\mathrm{U}$, manifesting the effect of target spin. The statistical saddle point model predictions underestimate the measured FF anisotropy for all four systems at measured energies. Anisotropy calculation by entrance channel dependent $K$-state distribution model and determination of $\langle {\ell }^2\rangle$ from continuum discretized coupled channels calculations suggest that the above enhancement in experimental anisotropy is due to a combined effect of entrance channel dependent pre-equilibrium fission and projectile breakup induced fission.

Figure 1

Fission fragment angular distributions for ${}^{6,7}\mathrm{Li}+{}^{235,238}\mathrm{U}$ systems measured at beam energies in the range of 28–42 MeV. Solid line corresponds to the fit using the standard expression (see text for details).

Figure 2

Angle integrated fission excitation functions for ${}^{6,7}\mathrm{Li}+{}^{235,238}\mathrm{U}$ reactions, showing larger cross sections for ${}^6\mathrm{Li}$ induced reactions (compared to ${}^7\mathrm{Li}$) at sub-barrier energies.

Figure 3

Fusion cross sections for ${}^{6,7}\mathrm{Li}+{}^{235,238}\mathrm{U}$ reactions calculated by coupled-channels calculations using ccdef [24] are compared with the measured fission/fusion cross sections.

Figure 4

Experimental (filled circles) and calculated fission fragment anisotropies as a function of center of mass energy for (a) ${}^6\mathrm{Li}$ $+{}^{235}\mathrm{U}$, (b) ${}^6\mathrm{Li}$ $+{}^{238}\mathrm{U}$, (c) ${}^7\mathrm{Li}$ $+{}^{235}\mathrm{U}$, and (d) ${}^7\mathrm{Li}$ $+{}^{238}\mathrm{U}$ reactions. Hollow circles represent the data from the literature [17]. Dashed lines correspond to the SSPM calculations. The ECD calculations with and without the spin of the target and projectile are represented by the solid and dash-dot-dot lines, respectively.

Figure 5

Experimental fission fragment anisotropies as a function of center of mass energy for (a) ${}^6\mathrm{Li}$ $+{}^{235,238}\mathrm{U}$ reactions and (b) ${}^7\mathrm{Li}$ $+{}^{235,238}\mathrm{U}$ reactions showing the effect of target dependence. Solid and dashed lines correspond to the entrance channel dependent (ECD) pre-equilibrium model calculated FF anisotropy for reactions involving the ${}^{235}\mathrm{U}$ and ${}^{238}\mathrm{U}$ targets, respectively.

Figure 6

Mean square angular momentum derived from FF anisotropy with and without effective $K_0^2$, denoted by ${\langle {\ell }^2\rangle }_{\mathrm{aniso}-\mathrm{C}}$ and ${\langle {\ell }^2\rangle }_{\mathrm{aniso}}$, are shown as filled and hollow circles, respectively, for (a) ${}^6\mathrm{Li}+{}^{235}\mathrm{U}$, (b) ${}^6\mathrm{Li}+{}^{238}\mathrm{U}$, (c) ${}^7\mathrm{Li}+{}^{235}\mathrm{U}$, and (d) ${}^7\mathrm{Li}+{}^{238}\mathrm{U}$ reactions. The same obtained from ccdef calculations (${\langle {\ell }^2\rangle }_{ccdef}$) and from fusion fit by Baba's method (${\langle {\ell }^2\rangle }_{\mathrm{fiss}}$) [40] are respectively shown as solid and dashed lines.

Figure 7

$K_0^2$ calculated from the Sierk model for ${}^6\mathrm{Li}$,${}^4\mathrm{He}$,${}^2\mathrm{H}$ $+{}^{238}\mathrm{U}$ systems.

Figure 8

Results of fresco calculations with (without) breakup coupling are shown as solid lines (dash-dot-dot lines) for (a,b) total fusion cross sections and (c,d) mean square angular momenta. Experimental angle integrated fission cross sections are shown as symbols for (a) ${}^6\mathrm{Li}$$+{}^{235,238}\mathrm{U}$ reactions (filled and hollow diamonds) and (b) ${}^7\mathrm{Li}$$+{}^{235,238}\mathrm{U}$ reactions (filled and hollow stars). Mean square angular momenta derived from FF anisotropy (${\langle {\ell }^2\rangle }_{\mathrm{aniso}}$) are shown as hollow circles for (c) ${}^6\mathrm{Li}+{}^{238}\mathrm{U}$ and (d) ${}^7\mathrm{Li}+{}^{238}\mathrm{U}$ reactions.