Probing isospin symmetry in the (Fe50, Mn50, Cr50) isobaric triplet via electromagnetic transition rates

Lifetimes of the $T=1$ isobaric analog ${I}^{\ensuremath{\pi}}={2}^{+}$ states in $^{50}\mathrm{Mn}$ and $^{50}\mathrm{Cr}$ were measured simultaneously by employing the recoil distance Doppler-shift (RDDS) technique. The states were populated in a fusion-evaporation reaction with a $^{12}\mathrm{C}$ beam on a $^{40}\mathrm{Ca}$ target. An analysis of the data and the calculations from the present work, together with the available $B(E2:{2}^{+}\ensuremath{\rightarrow}{0}^{+})$ data of the isobaric analog states in $^{50}\mathrm{Fe}$ and $^{50}\mathrm{Cr}$, were used to study isospin symmetry in the three $A=50$ isobaric nuclei. Shell-model calculations reproduce the magnitudes as well as the increasing trend of the $B(E2)$ data with increasing $Z$. To draw a firm conclusion on the level of isospin mixing in the triplet, a new precision measurement of the ${2}^{+}\ensuremath{\rightarrow}{0}^{+}$ transition rate in $^{50}\mathrm{Fe}$ will be required.