Seize the moment (or radius): What to do when your (long-range) observables don't converge?

Electric quadrupole (E2) observables are key to observing deformation and rotational collective structure in nuclei.  If ab initio nuclear theory is to provide insight into such collective structure, or provide a meaningful basis for comparison with experiment for the relevant E2 observables, then robust ab initio predictions for these observables are essential.  However, numerically meaningful, converged calculations for E2 observables are notoriously challenging to obtain in ab initio no-core configuration interaction (NCCI), or no-core shell model (NCSM), approaches.  Matrix elements of the E2 operator are sensitive to the large-distance tails of the nuclear wave function, which converge slowly in an oscillator basis expansion.

Nonetheless, the convergence patterns of calculated E2 matrix elements are often strongly correlated, especially in the case of matrix elements involving states with similar structure.  This suggests that meaningful predictions for the absolute scale of E2 observables may be made by calibrating to a single experimentally-known value.  Furthermore, the nuclear charge radius is similarly sensitive to the large-distance tails, and we can likewise consider calibrating E2 predictions to the measured charge radius.

In this talk, we shall explore the use of the measured ground state quadrupole moment and charge radius as calibration references for E2 predictions.  We shall illustrate by using this approach to provide robust ab initio predictions for several E2 transition strengths and quadrupole moments in p-shell nuclei, and compare these results against experimentally known values where available.