Quadrupole moments and proton-neutron structure in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math>-shell mirror nuclei
M. A. Caprio, Patrick J. Fasano, Pieter Maris, Anna E. McCoy
Abstract
Electric quadrupole ($E2$) matrix elements provide a measure of nuclear deformation and related collective structure. Ground-state quadrupole moments in particular are known to high precision in many $p$-shell nuclei. While the experimental electric quadrupole moment only measures the proton distribution, both proton and neutron quadrupole moments are needed to probe proton-neutron asymmetry in the nuclear deformation. We seek insight into the relation between these moments through the ab initio no-core configuration interaction (NCCI), or no-core shell model (NCSM), approach. Converged ab initio calculations for quadrupole moments are particularly challenging due to sensitivity to long-range behavior of the wave functions. We therefore study more robustly converged ratios of quadrupole moments: across mirror nuclides, or of proton and neutron quadrupole moments within the same nuclide. In calculations for mirror pairs in the $p$ shell, we explore how well the predictions for mirror quadrupole moments agree with experiment and how well isospin (mirror) symmetry holds for quadrupole moments across a mirror pair. The comparison with experiment confirms the predictive power of the ab initio description, indicating that the predicted ratios are physically relevant for understanding proton-neutron structure as well.