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We present a study on the isoscalar quadrupole strength in tin nuclei,focusing mainly on the low-energy region. The calculations are performed usingthe Skyrme type energy density functionals within the fully self-consistentquasiparticle random phase approximation, allowing for a good description ofthe experimental data for the first 2$^+$ state and the isoscalar giantquadrupole resonance. It is found that the first $2^+$ state and the low-energyquadrupole states between 3 and 6 MeV display an opposite behavior withincreasing neutron number. While the strength of the first $2^+$ statedecreases, some excited states start to accumulate between 3 and 6 MeV, andincrease their strength with increasing neutron number. This low-energy regionbetween 3 and 6 MeV is quite sensitive to the changes in the shell structurewith increasing neutron number. In particular, between $^{116}$Sn and$^{132}$Sn, the filling of the neutron orbitals with large values of $j$, hasan important impact on the low-energy region. Our analysis shows that thelow-energy states have a non-collective character, except the first 2$^+$state. In addition, the states in the low-energy region above 5 MeV display aninteresting pattern: with the increase of the neutron number, their strengthincreases and their nature changes, namely they switch from proton excitationsto neutron-dominated one. We conclude that the low-energy quadrupole statesbetween 3 and 6 MeV can provide information about the shell evolution inopen-shell nuclei.

Low-energy quadrupole states in neutron-rich tin nuclei