Isospin symmetry in $B(E2)$ values: Coulomb excitation study of ${}^{21}$Mg

Abstract: The $T_z$~=~$-\frac{3}{2}$ nucleus ${}<sup>{21}$Mg has been studied by Coulomb excitation on ${}<sup>{196}$Pt and ${}<sup>{110}$Pd targets. A 205.6(1)-keV $\gamma$-ray transition resulting from the Coulomb excitation of the $\frac{5}{2}<sup>+$ ground state to the first excited $\frac{1}{2}<sup>+$ state in ${}<sup>{21}$Mg was observed for the first time. Coulomb excitation cross-section measurements with both targets and a measurement of the half-life of the $\frac{1}{2}<sup>+$ state yield an adopted value of $$B(E2;\frac{5}{2}<sup>+\rightarrow\frac{1}{2}<sup>+)$$~=~13.3(4)~W.u. A new excited state at 1672(1)~keV with tentative $\frac{9}{2}<sup>+$ assignment was also identified in ${}<sup>{21}$Mg. This work demonstrates large difference of the $$B(E2;\frac{5}{2}<sup>+\rightarrow\frac{1}{2}<sup>+)$$ values between $T$~=~$\frac{3}{2}$, $A$~=~21 mirror nuclei. The difference is investigated in the shell-model framework employing both isospin conserving and breaking USD interactions and using modern \textsl{ab initio} nuclear structure calculations, which have recently become applicable in the $sd$ shell.