Multipole tomography of atomic nuclei with conserved symmetries

We introduce two-body nuclear conditional probabilities that allow the definition of an intrinsic reference frame and the multipole moments of angular-momentum-$J$-conserving states. This enables the characterization of quadrupole deformations of states with $J\leq1/2$, which are not accessible via spectroscopic one-body quadrupole moments. We illustrate the method with nuclear density functional theory (DFT) calculations for $J=0$ states of $^{16}$O and $^{20}$Ne, the latter obtained by restoring rotational symmetry of prolate or oblate intrinsic configurations. We show that the two-body quadrupole shape characterizations are not equal to the one-body moments obtained from broken-symmetry states, mainly because of Pauli repulsion effects. Calculations of two-body multipole moments can be performed within various theoretical frameworks, but their experimental determination requires measuring two-body correlations.