  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.
