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We explore two-particle transfer reactions as a unique probe of the occurenceof shape coexistence in shape phase transitions. The (t,p) reactions to theground state and to excited $0^+$ states are calculated for the isotope chainof even-even Zirconium isotopes starting from stable nuclei up to beyondcurrent experimental limits. Two-particle spectroscopic factors derived fromMonte Carlo Shell Model calculations are used, together with the sequentialdescription of the two-particle transfer reaction mechanism. The calculationshows a clear signature for a shape phase transition between $^{98}$Zr and$^{100}$Zr, which displays coexistence of a deformed ground state with anexcited spherical $0^+$ state. Furthermore, we show that there is a qualitativedifference with respect to the case of a normal shape phase transition that canbe discriminated with two-neutron transfer reactions.

Two-particle transfer processes as a signature of shape phase transition in Zirconium isotopes