Role of multi-phonon and high-spin states on the quasi-elastic barrier distributions of massive systems

Abstract

Back-angle quasi-elastic (QE) scattering provides critical barrier information in massive nuclear reactions leading to the synthesis of superheavy nuclei. The shapes and peaks of QE barrier distributions serve as fingerprints of nuclear structures and reaction dynamics. Couplings to collective movements can lead to distinctive peaks in the barrier distributions, but the role of multi-phonon and high-spin states has not been thoroughly investigated. In this work, we extend the high-accuracy R-matrix method and the finite element method to solve coupled-channel equations for massive systems. These two methods are demonstrated to be more stable than the widely used modified Numerov method and allows us to include more vibrational and rotational couplings. Using the reactions ${}^{48}\mathrm{Ti}$+${}^{208}\mathrm{Pb}$ and ${}^{51}V+{}^{248}\mathrm{Cm}$ as examples, calculations show that multi-phonon and high-spin states significantly smooth the barrier distributions, improving the agreement with experimental data. The comparison between the coupled-channel results and those obtained from the orientation average formula is examined. This work can advance the study of superheavy element synthesis by providing reliable barrier information and capture cross sections based on constraints from QE reactions.