The $T_z$~=~$-\frac{ 3}{ 2}$ nucleus ${ }^{ 21}$Mg has been studied by 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 $B(E2;\frac{ 5}{ 2}^+\rightarrow\frac{ 1}{ 2}^+)$~=~13.3(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 large difference of the $B(E2;\frac{ 5}{ 2}^+\rightarrow\frac{ 1}{ 2}^+)$ 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.
Categories: nucl-ex