Ab initio anatomy of quadrupole correlations in $^{16}$O and $^{20}$Ne

Abstract

Azimuthal hadronic flow measured in ultra-relativistic ion--ion collisions provides a new means of imaging multipole correlations in the ground state of atomic nuclei. Early interpretations largely relied on a classical-rotor picture, in which the measured mean-square elliptic flow is directly related to an intrinsic quadrupole deformation. Atomic nuclei, however, contain additional many-body correlations generated by the Pauli exclusion principle, collective shape fluctuations and non-collective dynamical processes, whose impact on this correspondence has not yet been elucidated. Here, we resolve this issue through an ab initio analysis of $^{16}$O and $^{20}$Ne based on chiral nuclear interactions, combining the in-medium similarity renormalization group with the quantum-number-projected generator coordinate method. By successively isolating antisymmetrization, collective rotational and vibrational, and non-collective dynamical correlations, we determine, for the first time, how each component contributes to the mean-square quadrupole eccentricity. We uncover an unexpected compensation among these distinct correlation mechanisms: despite sizable individual contributions, the squared effective quadrupole deformation inferred from the elliptic flow remains close to the square intrinsic deformation of the nucleus. This result provides a microscopic explanation for the surprising success of the classical-rotor approximation and establishes a quantitative foundation for interpreting $^{16}$O+$^{16}$O and $^{20}$Ne+$^{20}$Ne collision data recently collected at the Large Hadron Collider.