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We have studied, for the first time, the influence of the collective quantumeffects in the nuclear wave functions on the azimuthal anisotropy coefficients$\epsilon_{2,3}$ in the central Pb+Pb collisions at the LHC energies. With thehelp of the energy weighted sum rule we demonstrate that the classicaltreatment with the Woods-Saxon nuclear density overestimates the mean squarequadrupole moment of the $^{208}$Pb nucleus by a factor of $\sim 2.2$. TheMonte-Carlo Glauber simulation of the central Pb+Pb collisions accounting forthe restriction on the quadrupole moment leads to $\epsilon_2/\epsilon_3\approx0.8$ which allows to resolve the $v_2$-to-$v_3$ puzzle.

Collective nuclear vibrations and initial state shape fluctuations in central Pb+Pb collisions: resolving the $v_2$ to $v_3$ puzzle