Optical potentials for nuclear level structures and nucleon interactions data of tin isotopes based on the soft-rotator model

Abstract

The soft-rotator model is applied to self-consistent analyses of the nuclear level structures and the nucleon interaction data of the even-even Sn isotopes, $^{116}\mathrm{Sn}$, $^{118}\mathrm{Sn}$, $^{120}\mathrm{Sn}$, and $^{122}\mathrm{Sn}$. The model successfully describes low-lying collective levels of these isotopes, which exhibit neither typical rotational nor harmonic vibrational structures. The experimental nucleon interaction data---total neutron cross sections, proton reaction cross sections, and nucleon elastic and inelastic scattering data---are well described up to 200 MeV in a coupled-channels optical model approach. For the calculations, nuclear wave functions for the Sn isotopes are taken from the nonaxial soft-rotator model with the model parameters adjusted to fit the measured low-lying collective level structures. We find that the ${\ensuremath{\beta}}_{2}$ and ${\ensuremath{\beta}}_{3}$ deformations for incident protons are larger than those for incident neutrons by $~15%$, which is clear evidence of the deviation from the pure collective model for these isotopes.