Quantum coupled-channels model of nuclear fusion with a semiclassical consideration of neutron rearrangement

Abstract

Background: Significant enhancement of sub-barrier fusion cross sections owing to neutron transfer with positive $Q$ values was observed in many combinations of colliding nuclei. This degree of freedom has not yet been included into the rigorous quantum coupled-channels (QCC) approach. However, the empirical coupled-channels model with neutron rearrangement [Zagrebaev, Phys. Rev. C 67, 061601 (2003)] has already been successfully used in several papers to reproduce and predict cross sections for sub-barrier fusion reactions of stable nuclei.Purpose: The objective of this study is to combine the QCC approach and the empirical model to account for additional channels of neutron rearrangement.Method: Coupling of relative motion to collective degrees of freedom (rotation of nuclei and/or their surface vibrations) are taken into account within the QCC approach. The probability of transfer of $x$ neutrons with a given $Q$ value is estimated semiclassically.Results: The proposed new model was successfully tested on a few combinations of fusing nuclei $^{40}\text{Ca}+^{90,94,96}\text{Zr}, ^{32}\text{S}+^{90,94,96}\text{Zr}$, and $^{60,64}\text{Ni}+^{100}\text{Mo}$. The calculated fusion cross sections and barrier distribution functions agree well with experimental data.Conclusions: The model developed in this work confirms all the conclusions previously made within the empirical coupled-channels model with neutron rearrangement [see Rachkov et al., Phys. Rev. C 90, 014614 (2014)]. Moreover, it has an advantage of a more reliable microscopic account for the coupling between relative motion and the collective degrees of freedom. The proposed model can also be used to reproduce the structure of the barrier distribution function. This is a step forward to a complete solution of the long-term problem of accounting for neutron transfer channels in the QCC model.