Coulomb excitation of the $\left|T_zight|=\frac{1}{2}$, $A=23$ mirror pair

Background: Electric-quadrupole (E2) strengths relate to the underlying quadrupole deformation of a nucleus and present a challenge for many nuclear theories. Mirror nuclei in the vicinity of the line of N = Z represent a convenient laboratory for testing deficiencies in such models, making use of the isospin-symmetry of the systems. Purpose: Uncertainties associated with literature E2 strengths in 23 Mg are some of the largest in Tz = 1 2 nuclei in the sd-shell. The purpose of the present work is to improve the precision with which these values are known, to enable better comparison with theoretical models. Methods: Coulomb-excitation measurements of 23 Mg and 23 Na were performed at the TRIUMF-ISAC facility using the TIGRESS spectrometer. They were used to determine the E2 matrix elements of mixed E2/M 1 transitions. Results: Reduced E2 transition strengths, B(E2), were extracted for 23 Mg and 23 Na. Their precision was improved by factors of approximately six for both isotopes, while agreeing within uncertainties with previous measurements. Conclusions: A comparison was made with both shell-model and ab initio valence-space in-medium similarity renormalization group calculations. Valence-space in-medium similarity-renormalization-group calculations were found to underpredict the absolute E2 strength-in agreement with previous studies