Isospin dependence of electromagnetic transition strengths among an isobaric triplet

Electric quadrupole matrix elements, ${M}_{p}$, for the ${J}^{\pi }={2}^{+}\to {0}^{+}$, $\Delta T=0$, $T=1$ transitions across the $A=46$ isobaric multiplet $^{46}$Cr-$^{46}$V-$^{46}$Ti have been measured at GSI with the FRS-LYCCA-AGATA setup. This allows direct insight into the isospin purity of the states of interest by testing the linearity of ${M}_{p}$ with respect to ${T}_{z}$. Pairs of nuclei in the $T=1$ triplet were studied using identical reaction mechanisms in order to control systematic errors. The ${M}_{p}$ values were obtained with two different methodologies: (i) a relativistic Coulomb excitation experiment was performed for $^{46}$Cr and $^{46}$Ti; (ii) a "stretched target" technique was adopted here, for the first time, for lifetime measurements in $^{46}$V and $^{46}$Ti. A constant value of ${M}_{p}$ across the triplet has been observed. Shell-model calculations performed within the fp shell fail to reproduce this unexpected trend, pointing towards the need of a wider valence space. This result is confirmed by the good agreement with experimental data achieved with an interaction which allows excitations from the underlying sd shell. A test of the linearity rule for all published data on complete $T=1$ isospin triplets is presented.