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Simultaneous quadrupole and octupole shape phase transitions in Thorium

The evolution of quadrupole and octupole shapes in Th isotopes is studied in the framework of nuclear Density Functional Theory. Constrained energy maps and observables calculated with microscopic collective Hamiltonians indicate the occurrence of a simultaneous quantum shape phase transition between spherical and quadrupole-deformed prolate shapes, and between non-octupole and octupole-deformed shapes, as functions of the neutron number. The nucleus $^{224}$Th is closest to the critical point of a double phase transition. A microscopic mechanism of this phenomenon is discussed in terms of the evolution of single-nucleon orbitals with deformation.