Relative importance of energy dependent diffuseness parameter and barrier position in the analysis of fusion excitation function data

Abstract

Abstract.We have investigated the relative importance of the energy dependence of diffuseness parameter and barrier position in the description of the fusion excitation function data of some heavy ion systems in near barrier energy region. The effects of the energy dependent diffuseness parameter are found to be much more prominent in comparison to those of barrier position.The sub-barrier heavy ion fusion reactions provide a very good insight into nuclear structure and nuclear interaction [1][2][3][4]. The interaction potential between heavy ions which consists of Coulomb, centrifugal and nuclear terms plays a very crucial role in the description of fusion dynamics because of the fact that the sum of these terms forms the Coulomb barrier which must be overcome for occurrence of fusion. The Coulomb and centrifugal terms are well understood whereas many ambiguities are associated with the nuclear potential. Since the predictions of fusion excitation functions in sub-barrier energy regions are very sensitive to the shape of nuclear potential, the success of any model for fusion depends strongly on the nuclear potential model employed in the analysis. As a result various potential models ranging from the simple phenomenological to realistic microscopic models have been proposed and used to explain the fusion excitation functions data. Generally, the three parametric Woods-Saxon potential remains the most frequently used potential for the description of compound nuclear reactions. Among the three parameters, depth, range and diffuseness parameter, there exist, large ambiguities in the determination of the accurate value of the diffuseness parameter. It was observed that a wide range of values from 0.65 a fm  to fm a 5 . 1  of diffuseness parameter are required to describe various nuclear phenomena [5][6][7][8][9][10][11][12]. As the value of diffuseness parameter increases beyond 0.65 a fm  , the potential pocket becomes more and more shallow and disappears for large values and the fusion barrier radius decreases rapidly [6,[13][14][15]. Very recently, an energy dependent parameterization scheme to determine the value of diffuseness parameter was successfully used to explain the fusion excitation functions of various systems [16]. Since, the barrier position changes with the change in the shape of the potential, the energy dependent potential induces energy dependence in the barrier position also. ____________________________________________ a Corresponding

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

“…1. The fusion excitation functions of 32,36 16 S+ 90 40 Zr systems obtained by using the static Woods-Saxon potential model and energy-dependent Woods-Saxon potential model (EDWSP model) [18][19][20][21][22][23][24][25][26][27][28][29]. The results are compared with available experimental data (*) taken from Ref.…”

“…This abnormally large diffuseness might be an artifact of various kinds of static and dynamical physical effects such as fluctuation of densities and surface energy of colliding pairs. In this regard, the energy dependence in the Woods-Saxon potential is introduced via its diffuseness parameter and hence given by the following expression [18][19][20][21][22][23][24][25][26][27][28][29] a(E) = 0.85…”

“…Keeping this idea, the recent work undertook several efforts by analyzing the large set of the experimental data within the framework of energydependent Woods-Saxon potential model (EDWSP model) [18][19][20][21][22][23][24][25][26][27][28][29]. The closely similar physical effects that arise due to the internal structure of colliding pairs can be induced by entertaining the energy dependence in real part of nucleus-nucleus potential in such a way that it becomes more attractive at sub-barrier energies.…”

“…This energy-dependent nucleus-nucleus potential will effectively decrease the interaction barrier between fusing nuclei and hence predicts substantially larger sub-barrier fusion cross sections with reference to the energy-independent one-dimensional barrier penetration model as evident from the earlier work (EDWSP model). The introduction of the energy dependence in real part of nucleus-nucleus potential is also evident from the nucleon-nucleon interactions as well as from the non-local quantum effects [18][19][20][21][22][23][24][25][26][27][28][29]. The fusion dynamics of 32,36 16 S+ 90 40 Zr systems which are well studied in literature has been analyzed in the present work [30,31].…”

Static versus energy-dependent nucleus-nucleus potential for description of sub-barrier fusion dynamics of ${}_{8}^{16}{\rm O}+{}^{112,116,120}\!\!\!\!\!\!{}_{50}{\rm Sn}$ reactions

“…This diffuseness anomaly, which might be an artifact of different kinds of static and dynamical physical effects, reflects the systematic failure of the static Woods-Saxon potential in simultaneous exploration of the elastic scattering and the fusion data [1][2][3][4][5][6][7][25][26][27][28][29]. To understand the cause of the diffuseness anomaly and the puzzling behavior of sub-barrier fusion dynamics, our previous work has undertaken several attempts to study the fusion process within the framework of the energy-dependent Woods-Saxon potential model (EDWSP model) [30][31][32][33][34][35][36][37][38][39][40][41]. In heavy ion reactions, the closely similar physical effects that arise due to the internal structure of colliding pairs can be induced by incorporating the energydependence in the real part of the nucleus-nucleus potential so that it becomes more attractive at sub-barrier energies.…”