Atomic nuclei undergo rapid changes in structure, often characterized as transitions between “spherical” and “deformed” shapes, with small changes in the number of protons or neutrons. While it has long been known that shell closures drive spherical shapes and residual proton-neutron interactions drive collective motion and deformation, detailed theoretical studies that show how this competition leads to rapid nuclear structural changes have been challenging. This is particularly true for the $Z=64$ subshell closure, which affects the low-lying spectra and electric quadrupole transition strengths of the xenon, barium, cerium, neodymium, samarium, and gadolinium isotopic chains. Using a particle-number-conserved BCS theory and angular-momentum projection, we provide the first consistent description of the nuclear shape evolution and quantum phase transition among these nuclides. In particular, we find that the quasi-SU(3) couplings of the proton $0h_{11/2}\text{−}1f_{7/2}$ orbitals and the neutron $0i_{13/2}\text{−}1g_{9/2}$ orbitals, which are outside the usual model space, play a crucial role in overcoming the robustness of the $Z=64$ shell gap and initiating phase transitions. The neutron coupling is also essential for the gradual evolution in the heavier barium isotopes.

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• Collective levels
• Electromagnetic transitions
• Energy levels
• Nuclear structure & decays
• Phase transitions
• Shell model
• 150 ≤ A ≤ 189
• 90 ≤ A ≤ 149