Isospin symmetry in the lower $sd$ shell: Coulomb excitation study of ${}^{21}$Mg

Isospin symmetry was investigated in the lower $sd$ shell by studying the $T_z$ = $-frac{3}{2}$ nucleus ${}^{21}$Mg in Coulomb excitation on ${}^{196}$Pt and ${}^{110}$Pd targets. A 205.6(1)-keV $gamma$-ray transition resulting from the Coulomb excitation of the $frac{5}{2}^+$ ground state to the first excited $frac{1}{2}^+$ state in ${}^{21}$Mg was observed for the first time. Coulomb excitation cross-section measurements with both targets and a measurement of the half-life of the $frac{1}{2}^+$ state yield an adopted value of $B(E2;frac{5}{2}^+rightarrowfrac{1}{2}^+)$ = 12.7(4) W.u. A new excited state at 1672(1) keV with tentative $frac{9}{2}^+$ assignment was also identified in ${}^{21}$Mg. This work demonstrates the large deviation of the $B(E2;frac{5}{2}^+rightarrowfrac{1}{2}^+)$ values between $T$ = $frac{3}{2}$, $A$ = 21 mirror nuclei, predicted by a shell-model calculation employing a modified USD interaction. The new results are also compared to modern ab initio nuclear structure calculations, which have recently become applicable in the $sd$ shell.