Isospin-invariant Skyrme density functional investigation of quadrupole deformations in the isospin triplets of $\mathbf{A}=\mathbf{70},\mathbf{74}$ and $\mathbf{78}$

In this work, we perform self-consistent isospin-invariant Skyrme density functional calculations to investigate the ground-state properties of the isospin triplets with mass numbers $A=70$, $74$, and $78$. The present study is motivated by the reported anomaly between the observed quadrupole deformation and that expected from isospin symmetry. It is shown that the trend of the deduced $T_z$ dependence of $B(E2,2_1^{+}\to 0_1^{+})$ transition strengths from the charge quadrupole moments is consistent with the measured values for the $T_z=\pm 1$ members of the $A=70$ triplet. However, the calculated $B(E2,2_1^{+}\to 0_1^{+})$ rates for the $T_z=0$ members exceed the experimental transition rates in all the three studied triplets. Our study implies that non-linear dependence of the $B(E2,2_1^{+}\to 0_1^{+})$ transition strengths is expected in all of them and primarily arises from the observed suppressed transition rates for the $T_z=0$ members.