Effect of coupling in the ${}^{28}\mathrm{Si}+{}^{154}\mathrm{Sm}$ reaction studied by quasi-elastic scattering

The study of the coupling to collective states of the ${}^{28}\mathrm{Si}$ projectile and ${}^{154}\mathrm{Sm}$ target in fusion mechanism is reported. Understanding such couplings is important as they influence the barrier height and the formation probability of the compound nuclei, which in turn may be related to the synthesis of superheavy elements in heavier systems. In the present work, before performing the coupled-channel calculations, we wish to obtain an experimental signature of coupling to projectile and target excitation through barrier distribution (BD) study. To this end, the BDs of the ${}^{28}\mathrm{Si}+{}^{154}\mathrm{Sm}$ and ${}^{16}\mathrm{O}+{}^{154}\mathrm{Sm}$ systems have been compared using existing fusion data, scaled to compensate for the differences between the nominal Coulomb barriers and the respective coupling strengths. However, the large error bars on the high-energy side of the fusion BD prevent any definite identification of such signatures. We have, therefore, performed a quasi-elastic (QE) scattering experiment for the heavier ${}^{28}\mathrm{Si}+{}^{154}\mathrm{Sm}$ system and compared its results with existing QE data for the ${}^{16}\mathrm{O}$ projectile. Since QE BDs are precise at higher energies, the comparison has shown that the BD of ${}^{28}\mathrm{Si}+{}^{154}\mathrm{Sm}$ is similar to that of ${}^{16}\mathrm{O}+{}^{154}\mathrm{Sm}$ to a large extent except for a peaklike structure on the higher energy side. The similarity shows that the ${}^{154}\mathrm{Sm}$ deformation plays a major role in the fusion mechanism of ${}^{28}\mathrm{Si}+{}^{154}\mathrm{Sm}$ system. The peaklike structure is attributed to ${}^{28}\mathrm{Si}$ excitation. In contrast with previous studies, it is found that a coupled-channel calculation with vibrational coupling to the first $2^{+}$ state of ${}^{28}\mathrm{Si}$ reproduces this structure rather well. However, an almost identical result is found with the rotational coupling scheme if one considers the large positive hexadecapole deformation of the projectile. A value around that given by Möller and Nix $\left({\beta }_4\approx 0.25\right)$ leads to a strong cancellation in the re-orientation term that couples the $2^{+}$ state back to itself, making that state look vibrational in this process. Thus, unlike the existing fusion data, our new QE results contain subtle details about the fusion mechanism of ${}^{28}\mathrm{Si}+{}^{154}\mathrm{Sm}$ system. They even show a sensitivity to the ${}^{28}\mathrm{Si}$ hexadecapole deformation and hence may be capable of giving a physically reasonable estimate for ${\beta }_4$ in an indirect way.

Figure 1

Comparison of experimental fusion excitation functions (upper panels) and fusion barrier distributions (lower panels) for the systems ${}^{16}\mathrm{O}+{}^{154}\mathrm{Sm}$ and ${}^{28}\mathrm{Si}+{}^{154}\mathrm{Sm}$. Left-hand plots (a) and (b) are before scaling whereas the right-hand plots (c) and (d) show the comparison after scaling the ${}^{16}\mathrm{O}+{}^{154}\mathrm{Sm}$ data. In the right-hand plots an additional shift of 1.5 MeV for the ${}^{16}\mathrm{O}+{}^{154}\mathrm{Sm}$ system is seen to improve the overlap of the two data sets (see text).

Figure 2

Experimental setup for quasi-elastic measurements at two large backward angles, ${\theta }_{\mathrm{lab}}=170{}^{\circ }$ and $140{}^{\circ }$, for the ${}^{28}\mathrm{Si}+{}^{154}\mathrm{Sm}$ system.

Figure 3

Two-dimensional correlation plot of $\mathrm{\Delta }E\text{−}E$ energy signals from the hybrid telescope detector at $170{}^{\circ }$ with respect to the beam direction in the ${}^{28}\mathrm{Si}+{}^{154}\mathrm{Sm}$ reaction at $E_{\mathrm{lab}}=118\text{MeV}$. Projectile-like fragments of different atomic numbers are identified.

Figure 4

(a) Quasi-elastic excitation function and (b) corresponding barrier distribution obtained at two backward scattering angles, ${\theta }_{\mathrm{lab}}=170{}^{\circ }$ and $140{}^{\circ }$, for the ${}^{28}\mathrm{Si}+{}^{154}\mathrm{Sm}$ system.

Figure 5

Comparison of experimental QE excitation functions (upper panels) and corresponding barrier distributions (lower panels) for the systems ${}^{16}\mathrm{O}+{}^{154}\mathrm{Sm}$ and ${}^{28}\mathrm{Si}+{}^{154}\mathrm{Sm}$. Left-hand plots (a) and (b) are before scaling whereas right-hand plots (c) and (d) show the comparison after scaling the ${}^{16}\mathrm{O}+{}^{154}\mathrm{Sm}$ data and after applying a small extra shift (see text). The vertical dashed lines in panels (a) and (b) correspond to the position of the Bass barrier.

Figure 6

(a) Coupled-channels predictions compared with experimental QE excitation functions and (b) the resulting barrier distributions for the ${}^{28}\mathrm{Si}+{}^{154}\mathrm{Sm}$ system. The plot shows results obtained with vibrational (solid line) and rotational (dotted-dash line) couplings for the first $2^{+}$ state of ${}^{28}\mathrm{Si}$; the rotational calculation takes ${\beta }_4=0.1$.

Figure 7

Same as Fig. 6, but with the larger value of ${\beta }_4=0.25$ in the rotational coupling. Note the smoothing introduced by inclusion of the ${}^{154}\mathrm{Sm}$ octupole vibration.