Neutron transfer versus inelastic surface vibrations in the enhancement of sub-barrier fusion excitation function data and the energy dependent Woods–Saxon potential

Abstract

This work deeply analyzed the relative importance of the neutron transfer channels and inelastic surface vibrations of colliding nuclei in the sub-barrier fusion enhancement of various heavy ion systems using an energy dependent Woods-Saxon potential (EDWSP) model in conjunction with a one-dimensional Wong formula and the coupled channel formulation using the code CCFULL. The multi-phonon vibrational states of colliding nuclei and the nucleon transfer channels are found to be dominant internal degrees of freedom. The coupling between the relative motion of reactants and these relevant channels produces anomalously large sub-barrier fusion enhancement over the expectations of the one-dimensional barrier penetration model. In some cases, the influence of neutron transfer dominates over the couplings to low lying surface vibrational states of collision partners. Furthermore, the effects of coupling to inelastic surface excitations and the impact of neutron transfer channels with positive ground state Q-values are imitated due to energy dependence in the Woods-Saxon potential. In the EDWSP model calculations, a wide range for the diffuseness parameter, which is much larger than the value extracted from the elastic scattering data, is needed to account for the observed fusion enhancement in the close vicinity of the Coulomb barrier. Keywords: heavy-ion near-barrier fusion reactions, depth and diffuseness of Woods-Saxon potential, coupled channel equations, diffuseness anomaly

Systematic failure of static nucleus–nucleus potential to explore sub-barrier fusion dynamics

“…This kind of physical effect is a Table 3. Range, depth and diffuseness of the Woods-Saxon potential used in the EDWSP model calculations for various heavy ion systems [29][30][31][32][33][34][35][36][37][38][39][40]. direct manifestation of the enhancement of the fusion crosssection at energies below the energy of the uncoupled barrier.…”

Role of Barrier Modification and Inelastic Surface Excitations in Sub-Barrier Fusion of 16 32 S + 40 94 Zr Reaction

“…To resolve the puzzling features of the fusion dynamics of the 16 32 S + 40 94 Zr system, this work compares the predictions of different theoretical methods. The static Woods-Saxon potential in conjunction with one-dimensional Wong formula [24] fails to explain the fusion dynamics of this system, while the predictions of the EDWSP model [17][18][19][20][21] successfully explain the observed fusion dynamics of 16 32 S + 40 94 Zr system. In addition, the role of different Skyrme interactions such as SIII and GSkI within the context of one-dimensional Wong and ℓ-summed extended Wong formula [25][26][27][28] is also tested for the description of the observed sub-barrier fusion enhancement of 16 32 S + 40 94 Zr system.…”

“…Hence, more intensive investigations are required to address this issue. In this regard, several attempts have been made to understand the cause of the diffuseness anomaly as well as the systematic failure of the static Woods-Saxon potential by introducing the energy dependence in the real part of nuclear potential in such a way that it becomes more attractive at sub-barrier energies [17][18][19][20][21]. This energy dependence in the nucleus-nucleus potential in turn induces closely similar physical effects that arise due to the coupling between the relative motion and the internal degrees of freedom of the colliding pairs.…”

“…Therefore, it is reasonable to test the applicability of the energydependent nucleus-nucleus potential for the description of the sub-barrier fusion dynamics. Following this idea, the energydependent Woods-Saxon potential model (EDWSP model) was introduced, wherein the energy dependence in the Woods-Saxon potential was taken via its diffuseness parameter [17][18][19][20][21].…”

“…The EDWSP model includes the effects of the surface energy as well as the isospin asymmetry of colliding pairs [17][18][19][20][21]. The various channel coupling effects responsible for sub-barrier fusion enhancement are the surfacial effects, and during collisions, they modify the surface diffuseness as well as the surface energy of the collision partners and hence bring the requirement of larger diffuseness parameter to address the fusion excitation function data [1-3, 7-11, 16].…”