Quadrupole moments and proton-neutron structure in p-shell mirror nuclei

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 protonneutron 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.

Remeasuring the anomalously enhanced $B(E2; 2^+ \rightarrow 1^+)$ in $^8$Li and comparison to \textit{ab initio} predictions

“…4(a) of Ref. [28]], giving B(E2; a generally more tractable convergence is obtained for this ratio, which rapidly converges to a value independent of N max and ω at the scale shown. Similar results for the B(E2)/(eQ) 2 ratios involving in-band transitions in the neighboring nuclides 7 Li, 7 Be, and 9 Be are shown in Fig.…”

“…For 7 Be, although the ground state quadrupole moment is not experimentally known [23], we may make a primitive estimate. Simply substituting 3 He for 3 H in the cluster description gives a quadrupole moment for 7 Be larger than that of 7 Li by a factor of ∼ 1.47 [28]. 1 To preserve the rotational value for the ratio B(E2)/(eQ) 2 , we would thus need the E2 strength in 7 Be to be larger than that in 7 Li by a factor of ∼ 2.3.…”

“…However, commonly even an order-ofmagnitude estimate is elusive (see, e.g., Ref. [28], for further examples).…”

“…Further details, including illustrations of the convergence properties of E2 observables obtained with these different interactions, may be found in Ref. [28].…”

“…These moments provide a rotational normalization for the E2 strength: ratios of the form B(E2)/(eQ 2 ) within a rotational band are given by the rotational Alaga rules [24][25][26]. Taking such ratios of E2 matrix elements cancels out systematic normalization uncertainties arising (from incomplete convergence) in ab initio calculations [16,27,28].…”