Quadrupole Strength in Isobaric Triplets
The dependence of the $E2$ matrix elements on isospin projection $T_z$ is linked to the conservation of the isospin symmetry. To study this conjecture, we calculated the ${B(E2: 2^+ \rightarrow 0^+)}$ rates for the even-even $T=1$ mirror nuclei with $42$ $\leq$ $A$ $\leq$ $98$ within nuclear density functional theory, employing the generalized Bohr Hamiltonian, and carrying out angular momentum projection. We demonstrated that collective effects are crucial for describing experimental data near the $N=Z$ line without invoking explicit beyond-Coulomb isospin symmetry-breaking corrections. We also determined the $B(E2\downarrow)$ values for odd-odd $T_z=0$ nuclei $^{70}Br$ and $^{78}Y$ in doubly-blocked configurations. We discussed the requirements for accurately describing isobaric analog states and emphasized how current theoretical results should be interpreted within the study of isospin symmetry across isospin triplets.