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The electromagnetic features of the $11/2^-$ isomers in the $^{111-127}$Cdisotopes are reproduced by numerically optimized shell-model wave-functions. Asudden phase change of the wave functions at $N = 70$ is identified and furtherconfirmed by the evolution of B(E2, $7/2^-_1\rightarrow 11/2^-_1$) values. Thisphase change gives rise to different linear relations for the $Q$ and $\mu$values with $N<70$ and $N>70$, as needed to reproduce the experimental data.The particle-hole transformation properties for $h_{11/2}$ neutrons in awell-isolated subshell involving degenerate $s_{1/2}$, $d_{3/2}$, $d_{5/2}$ and$h_{11/2}$ orbits is suggested as a possible explanation for this phase change.

Phase change near $N=70$ in the wave function of the $I^{\pi}=11/2^-$ isomers along the cadmium-isotope chain