Role of Inelastic Surface Excitations and the Energy-dependent Woods--Saxon Potential in Sub-barrier Fusion of $_{\ \ \,16}^{32,36}$S$+^{90}_{40}$Zr Reactions

Abstract

The static nucleus-nucleus potential and the energy-dependent nucleusnucleus potential are used to address the sub-barrier fusion reactions. The static nucleus-nucleus potential systematically fails to recover the experimental data of 32,36 16 S+ 90 40 Zr systems. However, the energy-dependent Woods-Saxon potential model (EDWSP model) in conjunction with the one-dimensional Wong formula accurately addresses the sub-barrier fusion enhancement of these systems. The role of the inelastic surface excitations of collision partners in the fusion dynamics is entertained within the context of coupled channel calculations performed by using coupled channel code CCFULL. It is worth noting here that the energy dependence in nucleusnucleus potential simulates the effects of inelastic surface excitations of colliding nuclei in the sub-barrier fusion enhancement of 32,36 16 S+ 90 40 Zr systems.

Role of Projectile Degrees of Freedom in Sub-Barrier Fusion Dynamics

“…The values of range parameter used in the EDWSP model calculations are consistent with the commonly adopted values of the range parameter (r 0 = 0.90fm to r 0 = 1.35fm) used in literature within the context of the different theoretical methods for different fusing systems [1,2,[35][36][37][38][39][40][41][42]. In the present analysis, the values of the range parameter extracted for the 4 9 Be + 39 89 Y, Y reactions are also consistent with our previous analysis [23][24][25][26][27][28][29][30][43][44][45][46][47].…”

“…The comparison of the fusion excitation functions of the 4 9 Be + 39 89 Y, 6 12 C + 39 89 Y, and 16 32,34 S + 39 89 Y reactions reveals that the above barrier fusion excitation function data of the 4 9 Be + 39 89 Y reaction is suppressed with reference to that of the 6 12 C + 39 89 Y and 16 32,34 S + 39 89 Y reactions [21,22]. The theoretical calculations of the fusion excitation functions are obtained using the energydependent Woods-Saxon potential model (EDWSP model) [23][24][25][26][27][28][29][30] and the coupled channel approach [31]. The single barrier penetration model calculations and the coupled channel calculations predict larger fusion cross sections for the 4 9 Be + 39 89 Y reaction by an amount of 20 % at above barrier energies.…”

“…In the recent work, the EDWSP model [23][24][25][26][27][28][29][30] has been exploited to explain the observed fusion dynamics of tightly bound systems wherein it has shown that the energy dependence in nucleus-nucleus potential introduces similar kinds of the barrier modification effects as evident from the usual coupled channel approach. This work has been extended to explore the fusion dynamics of the projectile-target combinations involving weakly bound system.…”

“…Fig.1The fusion barrier (FB) for the16 32,34 S + 39 89 Y reactions obtained using the EDWSP model[23][24][25][26][27][28][29][30] …”

Role of projectile breakup effects and intrinsic degrees of freedom on fusion dynamics

“…The target isotopes ( 90,94 Zr) are spherical in shape and exhibit low lying inelastic surface vibrational states as the dominant mode of couplings. The fusion dynamics of 28 Si+ 90,94 Zr reactions is expected to behave in a similar way to that of 32,36 S + 90,96 Zr and 40,48 Ca + 90,96 Zr reactions [39,40] wherein the role of multi-neutron transfer channels have been precisely identified. In the fusion of the 28 Si+ 90 Zr reaction, the inclusion of the collective surface vibrational states of fusing systems produces substantially large sub-barrier fusion enhancement over the expectations of the one dimensional barrier penetration model [36][37][38].…”