Pseudospin Symmetry and Microscopic Origin of Shape Coexistence in the $^{78}$Ni Region: A Hint from Lifetime Measurements

Lifetime measurements of excited states of the light $N=52$ isotones $^{88}$Kr, $^{86}$Se, and $^{84}$Ge have been performed, using the recoil distance Doppler shift method and VAMOS and AGATA spectrometers for particle identification and gamma spectroscopy, respectively. The reduced electric quadrupole transition probabilities $B(E2;2^+ \rightarrow 0^+)$ and $B(E2;4^+ \rightarrow 2^+)$ were obtained for the first time for the hard-to-reach $^{84}$Ge. While the $B(E2;2^+ \rightarrow 0^+)$ values of $^{88}$Kr, $^{86}$Se saturate the maximum quadrupole collectivity offered by the natural valence $(3s, 2d, 1g_{7/2}, 1h_{11/2})$ space of an inert $^{78}$Ni core, the value obtained for $^{84}$Ge largely exceeds it, suggesting that shape coexistence phenomena, previously reported at $N \lesssim 49$, extend beyond $N=50$. The onset of collectivity at $Z=32$ is understood as due to a pseudo-SU(3) organization of the proton single-particle sequence reflecting a clear manifestation of pseudospin symmetry. It is realized that the latter provides actually reliable guidance for understanding the observed proton and neutron single particle structure in the whole medium-mass region, from Ni to Sn, pointing towards the important role of the isovector-vector $\rho$ field in shell-structure evolution.