Reaffirmation of probe dependence of the mass deformation length for low-lying excitations in Sn112,116,118,120,122,124 isotopes

Background: A transparent approach for the study of nuclear shapes and sizes in excited states requires knowledge about dynamic deformations of both neutron and proton distributions, by means of their independent excitations at the same energy. Heavy-ion scattering could be a reliable approach, facilitating a simultaneous study of deformations of charge and matter densities in nuclei.Purpose: Measurement of angular distributions of the inelastic scattering cross sections for excitations to low-lying ${2}_{1}^{+}$ and ${3}_{1}^{\ensuremath{-}}$ states in $^{112,116,118,120,122,124}\mathrm{Sn}$ nuclei using $^{12}\mathrm{C}$ beam as a probe at ${E}_{\mathrm{lab}}=60\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$, and determination of neutron and proton transition matrix elements involved in each excitation.Methods: Projectilelike fragments have been detected using ten sets of Si-surface barrier detector telescopes to measure the cross sections for elastic and inelastic scattering channels. Coupled reaction channels calculations are performed to understand the measured differential cross sections.Results: Homogeneous nature of surface vibrations (similar deformation for proton and neutron distributions) for the ${2}_{1}^{+}$ and ${3}_{1}^{\ensuremath{-}}$ states in Sn isotopes is observed.Conclusions: A comparison with recent results using $^{7}\mathrm{Li}$ projectile at similar ${E}_{\mathrm{c}.\mathrm{m}.}/{V}_{\mathrm{B}}$, which showed damped neutron vibrations particularly for the ${3}_{1}^{\ensuremath{-}}$ state, confirms that such measurements are probe dependent. Intrinsic transition matrix elements of nuclei can be deduced by removing the effects of finite projectile size in the extraction of nuclear shapes.