Influence of neutron transfer channels and collective excitations in the fusion of Si28 with Zr90,92,94,96 targets

This work theoretically explores the role of neutron transfer channels and/or collective inelastic surface excitations in the fusion of $^{28}\mathrm{Si}$ with $^{90,92,94,96}\mathrm{Zr}$ targets by using the coupled channel theory and the energy dependent Woods-Saxon potential (EDWSP) model. The series of $^{90,92,94,96}\mathrm{Zr}$ targets is quite interesting due to the fact that the possibilities of neutron transfer channels with positive ground state $Q$ values increase with the increase of isotopic mass. For $^{28}\mathrm{Si}+^{90}\mathrm{Zr}$ reaction, the influences of inelastic surface excitations turned out to be important and coupling of such channels to their relative motion reproduced the experimental data. In the case of $^{28}\mathrm{Si}+^{92}\mathrm{Zr}$ reaction, in addition to consideration of low lying states such as ${2}^{+}$ and ${3}^{\ensuremath{-}}$ vibrational states of colliding nuclei, the coupling to two neutron pickup channels is necessarily required to address the sub-barrier fusion anomalies. For $^{28}\mathrm{Si}+^{94,96}\mathrm{Zr}$ reactions, the inclusions of multiphonon states of type ${2}^{+}$ and ${3}^{\ensuremath{-}}$ of colliding nuclei were not able to reproduce the fusion enhancement particularly at below barrier energies. In this case, neutron transfer channels with positive ground state $Q$ value play a crucial role in the enhancement of fusion cross-section data at sub-barrier energies and therefore must be included in the coupled channel description. In distinction, in the EDWSP model, the energy dependence in the nucleus-nucleus potential causes barrier modification effects and subsequently induces a barrier lowering phenomenon. In this way, the EDWSP based outcomes reasonably address the sub-barrier fusion anomalies of $^{28}\mathrm{Si}+^{90,92,94,96}\mathrm{Zr}$ reactions and thus impacts of dominant intrinsic channels are intrinsically included due to the dynamical nature of the energy dependent interaction potential. For studied systems, the EDWSP outcomes are able to achieve an agreement with the portion of above barrier fusion data within 10% with a probability greater than 90%. Within this model, 33 fusion data points out of 38 fusion data points lie within 5%. Only five fusion data points lie within 10% and thereby the EDWSP model adequately addresses the fusion anomalies of the chosen reactions. The smaller values of ${\ensuremath{\chi}}^{2}$ analysis for the EDWSP calculations, which range from 2.82 to 3.14, indicate that the model predictions appropriately describe the observed fusion dynamics of the studied reactions.