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

Abstract

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 ${\hat{I}}^3$-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 $B(E2;{\frac{5}{2}}^{+}\to {\frac{1}{2}}^{+})$~=~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 $B(E2;{\frac{5}{2}}^{+}\to {\frac{1}{2}}^{+})$ 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.

8 pages, 6 figures, submitted to Phys. Rev. C, Rapid Communication