Ab initio estimation of $E2$ strengths in $^8$Li and its neighbors by normalization to the measured quadrupole moment

TL;DR

This paper introduces a method to predict electric quadrupole ($E2$) transition strengths in light nuclei by normalizing to known quadrupole moments, improving the reliability of ab initio calculations with slow convergence.

Contribution

The authors propose a normalization approach to estimate $E2$ strengths in nuclei, using measured quadrupole moments to calibrate ab initio calculations, demonstrated on lithium and beryllium isotopes.

Findings

The proportionality of $E2$ matrix elements within the same rotational band.

Calibration to the ground-state quadrupole moment improves $E2$ predictions.

Predicted $E2$ transition strength in $^8$Li matches experimental data better than previous models.

Abstract

For electric quadrupole ($E2$) observables, which depend on the large-distance tails of the nuclear wave function, ab initio no-core configuration interaction (NCCI) calculations converge slowly, making meaningful predictions challenging to obtain. Nonetheless, the calculated values for different $E2$ matrix elements, particularly those involving levels with closely-related structure (e.g., within the same rotational band) are found to be robustly proportional. This observation suggests that a known value for one observable may be used to determine the overall scale of $E2$ strengths, and thereby provide predictions for others. In particular, we demonstrate that meaningful predictions for $E2$ transitions may be obtained by calibration to the ground-state quadrupole moment. We test this approach for well-measured low-lying $E2$ transitions in $^7$Li and $^9$Be, then provide predictions for transitions in $^8$Li and $^9$Li. In particular, we address the $2^+\rightarrow1^+$ transition in $^8$Li, for which the reported measured strength exceeds ab initio Green's function Monte Carlo (GFMC) predictions by over an order of magnitude.