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

Abstract

This paper addresses the validity of the static Woods-Saxon potential and the energy dependent Woods-Saxon potential (EDWSP) for description of sub-barrier fusion dynamics. The low lying surface vibrations of colliding nuclei and neutron transfer channels are found to be major factors responsible for fusion enhancement at sub-barrier energies. Theoretical calculations based upon the static Woods-Saxon potential obtained using the one-dimensional Wong formula fail to explain the energy dependence of the sub-barrier fusion cross-section of + Ca Ti 40 20 46,48,50 22 Keywords: depth and diffuseness of Woods-Saxon potential, coupled channel equations, heavyion sub-barrier fusion reactions, diffuseness anomaly

Effects of intrinsic degrees of freedom in enhancement of sub-barrier fusion excitation function data and energy-dependent one-dimensional barrier penetration model

“…In the previous work, the energy-dependent Woods-Saxon potential model (EDWSP model) has been successfully used to address the role of inelastic surface vibrations of colliding pairs and the multi-neutron transfer channels [21][22][23][24][25][26][27][28][29][30][31][32][33]. The form of static Woods-Saxon potential is defined as…”

“…The present parameterization of potential depth is based upon the reproduction the fusion excitation function data of wide range of projectile-target combinations ranging from Z P Z T = 84 to Z P Z T = 1640 [21][22][23][24][25][26][27][28][29][30][31][32][33]. In fusion process, the various kinds of static and dynamical physical effects such as variations of densities of colliding nuclei, dissipation of kinetic energy of relative motion into internal structure degrees of freedom, different kinds of channel couplings effects (influences of inelastic surface vibrational states, rotational states of deformed nuclei, multi-nucleon transfer channels) or other static and dynamical physical effects occur in the surface region of nuclear potential or in the tail region of Coulomb barrier.…”

“…(6), which is directly proportional to surface energy of the colliding nuclei, accommodates such static and dynamical physical effects. All these physical effects bring the necessity of larger diffuseness parameter ranging from a = 0.75 fm to a = 1.5 fm for accounting the sub-barrier fusion data [21][22][23][24][25][26][27][28][29][30][31][32][33]. In addition, the isotopic effects are generally evident if a common projectile is bombarded on a series of target isotope or vice versa, and these isotopic effects are incorporated in the present model via isospin of colliding nuclei.…”

“…The role of internal structure degrees of freedom of colliding nuclei is entertained within the framework of coupled channel calculations performed by using the code CCFULL [34]. In EDWSP model, the energy dependence of Woods-Saxon potential induces similar kinds of static and dynamical physical effects as deduced from the channel coupling effects and hence brings the larger fusion enhancement at below-barrier energies with respect to the energy-independent one-dimensional barrier penetration model as evident from the earlier works [21][22][23][24][25][26][27][28][29][30][31][32][33].…”

“…This diffuseness anomaly, which reflects the inconsistency of static Woods-Saxon potential for simultaneously exploring of elastic scattering and fusion process, may be associated with various kinds of static and dynamical physical effects [1][2][3][4][5][6][7][18][19][20]. To understand the cause of diffuseness anomaly and the puzzling behavior of sub-barrier fusion data, in the present work we have analyzed the fusion dynamics of 32;36 16 S þ 90;96 40 Zr systems within the context of the coupled channel approach and the energy-dependent Woods-Saxon potential model (EDWSP model) [21][22][23][24][25][26][27][28][29][30][31][32][33]. The role of internal structure degrees of freedom of colliding nuclei is entertained within the framework of coupled channel calculations performed by using the code CCFULL [34].…”