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

We have studied, for the first time, the influence of the collective quantum effects in the nuclear wave functions on the azimuthal anisotropy coefficients $\epsilon_{2,3}$ in the central Pb+Pb collisions at the LHC energies. With the help of the energy weighted sum rule we demonstrate that the classical treatment with the Woods-Saxon nuclear density overestimates the mean square quadrupole moment of the $^{208}$Pb nucleus by a factor of $\sim 2.2$. The Monte-Carlo Glauber simulation of the central Pb+Pb collisions accounting for the restriction on the quadrupole moment leads to $\epsilon_2/\epsilon_3\approx 0.8$ which allows to resolve the $v_2$-to-$v_3$ puzzle.