Low-lying quadrupole and octupole collective excitations in the Sn112,116,118,120,122,124 isotopes

Abstract

Background: In recent years, considerable interest has been focused on the study of the effect of neutron skin on the collective properties of vibrational nuclei. This can be best evidenced by exclusively determining neutron and proton transition matrix elements involved in a particular excitation by investigating the Coulomb-nuclear interference feature of inelastic scattering.Purpose: Measurement of angular distributions of the inelastic scattering cross sections for excitations to low-lying ${2}_{1}^{+}$ and ${3}_{1}^{\ensuremath{-}}$ states in $^{112,116,118,120,122,124}\mathrm{Sn}$ using $^{7}\mathrm{Li}$ beam as probe at ${E}_{\mathrm{lab}}=28\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ and determination of neutron and proton transition matrix elements involved in each excitation.Methods: Projectilelike fragments were detected using six sets of Si-surface barrier detector telescopes to measure the cross sections for elastic and inelastic scattering channels. Optical model analysis of elastic scattering data, coupled reaction channels, and continuum discretized coupled channels calculations were performed to understand the measured differential cross sections. An attempt has been made to extract the microscopic mass and charge deformation lengths.Results: For the ${2}_{1}^{+}$ state, experimental $B(E2)$ values are in good agreement with existing results obtained by electromagnetic methods. Charge and mass quadrupole vibrations are homogeneous. Significant differences are observed for excitation to the ${3}_{1}^{\ensuremath{-}}$ state across the Sn isotopic chain. Available structural information for collective octupole vibrations could not reproduce the present data for this excitation. Results show much lower values of octupole mass deformation parameters.Conclusions: Isoscalar nature of surface vibrations for the ${2}_{1}^{+}$ state in Sn isotopes is verified, with ${M}_{n}/{M}_{p}\ensuremath{\sim}N/Z$. For the ${3}_{1}^{\ensuremath{-}}$ state, damped mass vibration is the primary observation. On comparison with existing estimates, a significant deviation from isoscalar nature is conjectured for this excitation, when probed with $^{7}\mathrm{Li}$.