Barrier distribution functions for the system ${}^6\mathrm{Li}+{}^{64}\mathrm{Ni}$ and the effect of channel coupling

Background: The barrier distribution function is an important observable in low-energy nucleus-nucleus collisions because it carries the distinct signature of the channel-coupling effect that is dominant at low energies. It can be derived from the fusion excitation function as well as from the back-angle quasi-elastic excitation function. The barrier distribution functions derived from the two complimentary measurements, in general, appear to peak at an energy close to the Coulomb barrier for strongly bound systems. But for weakly bound projectiles, like ${}^6\mathrm{Li}$, a relative shift is observed between the distributions.

Purpose: The present work investigates the barrier distribution functions from fusion as well as from the back-angle quasi-elastic excitation function for the ${}^6\mathrm{Li}+{}^{64}\mathrm{Ni}$ system. The purpose is to look for the existence of a shift, if any, between the two measured distribution functions, as reported for ${}^6\mathrm{Li}$ collision with heavy targets. A detailed coupled-channel calculation to probe the behavior of the distribution functions and their relative shift has been attempted.

Measurement: A simultaneous measurement of fusion and back-angle quasi-elastic excitation functions for the system ${}^6\mathrm{Li}+{}^{64}\mathrm{Ni}$ was performed. The fusion excitation function was measured for the energy range of 11 to 28 MeV while the quasi-elastic excitation function measurement extended from 11 to 20 MeV. The barrier distribution functions were subsequently extracted from both the excitation functions and compared.

Results: A small shift of around 450 keV peak to peak is observed between the barrier distribution functions derived from the complementary measurements. Detailed coupled channel and coupled reaction channel calculations reproduced both the excitation functions and barrier distributions. The shift of about 550 keV resulted from the model predictions corroborate the experimentally observed value for ${}^6\mathrm{Li}+{}^{64}\mathrm{Ni}$ system.

Conclusions: The coupling to inelastic channels are found to be sufficient to describe the fusion-barrier distribution. The positive $Q$-value one-proton and one-neutron stripping channels, leading to three-body final states, on the other hand, play dominant roles in reproducing the barrier distribution from the back-angle quasi-elastic excitation function.

Figure 1

The energy spectrum of the ejectile at ${\theta }_{\mathrm{lab}}={150}^{\circ }$ for $E_{\mathrm{lab}}=16$ MeV. The two solid lines indicate the limits of the region considered for the estimation of quasi-elastic yield. The long dashed line on the left corresponds to the energy of the $\alpha$ particle moving with beam velocity in the direction of ${\theta }_{\mathrm{lab}}={150}^{\circ }$ after the breakup of ${}^6\mathrm{Li}$. The dashed-dotted and short dashed lines indicate the energies of $\alpha$ particles moving with the same velocities as the unstable ${}^5\mathrm{Li}$ and ${}^5\mathrm{He}$ ejectiles in the direction of ${\theta }_{\mathrm{lab}}={150}^{\circ }$ following the $1n$- and $1p$-stripping reactions, respectively. The shaded regions marked by $bu,n$, and $p$ represent the energy ranges of $\alpha$ particles coming from sequential breakup, $1n$-, and $1p$-stripping reactions.

Figure 2

(a) The experimental fusion excitation function has been shown in comparison with the one dimensional barrier penetration model (1DBPM) and CC model predictions. (b) Corresponding barrier distribution functions (DB). The energy values include the target thickness correction and the uncertainty restricted within the width of the symbol.

Figure 3

Back angle (${\theta }_{\mathrm{lab}}={150}^{\circ }$) quasi-elastic excitation function plotted in upper panel. The quasi-elastic cross section was estimated using the yields under the peaks marked in Fig. 1. The yields under consideration predominantly comes from the elastic scattering and inelastic scattering form the 1.345 MeV first-excited state of ${}^{64}\mathrm{Ni}$. In the lower panel, the derived data of quasi-elastic barrier distribution has been shown by solid squares. For comparison, the fusion-barrier distribution obtained from the TF excitation function has been shown by open circles. $DB$ denotes barrier distribution function in the lower panel. The energy values corresponding to fusion barrier distribution includes the correction due to the target thickness while that corresponding to the quasi-elastic distribution includes target thickness as well as centrifugal correction of Eq. (4).

Figure 4

The quasi-elastic excitation functions from CRC calculation with different coupling conditions in comparison with the data ($\blacksquare$). The dashed-dotted curve represents the excitation function in no coupling condition. The CC I (dotted) curve stands for inelastic coupling only while CC II (dashed-double dotted) stands for the condition $\text{CC}\text{I}+1n$ stripping. The CC III (dashed curve) condition denotes the coupling scheme of $\text{CC}\text{I}+1p$ stripping and CC IV (solid curve) is for the coupling scheme that includes inelastic, $1n$- and $1p$-stripping channels.

Figure 5

The barrier distribution extracted from the calculated quasi-elastic excitation functions in comparison derived barrier distribution data ($\blacksquare$). For the description of the curves, see Fig. 4.

Figure 6

The experimental quasi-elastic excitation function (upper panel) and corresponding barrier distribution function (denoted by $DB$ in the lower panel) compared with the CRC calculation that includes the coupling to positive parity ${\frac{9}{2}}^{+}$ states in residues ${}^{65}\mathrm{Cu}$ and ${}^{65}\mathrm{Ni}$ from the reactions $({}^6\mathrm{Li},{}^5\mathrm{He})$ and $({}^6\mathrm{Li},{}^5\mathrm{Li})$ along with the coupling scheme CC IV (see text).