Two-particle transfer reactions: a key tool for the study of phase transitions in nuclei

In this talk I discuss the possible use of two-particle transfer intensities as a signature of sharp shape transitions. I first consider simple models of phase transitions based on algebraic bosonic approaches, including the case of shape coexistence, showing a dramatic change in the pair-transfer probabilities in correspondence of the critical points. Moving then to a microscopic description of both structure and reaction aspects, I consider as an example the complete series of (t,p) reactions populating the isotope chain of even Zirconium nuclei, to the ground state and to excited 0⁺ states. One- and two-particle spectroscopic factors derived from Monte Carlo Shell Model calculations are used, together with the sequential description of the two-particle transfer reaction mechanism. The calculation shows a clear signature for a shape phase transition between the spherical ⁹⁸Zr and ¹⁰⁰Zr, which displays a coexistence of a deformed ground state with an excited spherical 0+ state. As a result one predicts a weak two particle cross section from the spherical ⁹⁸Zr to the deformed ground state of ¹⁰⁰Zr, with instread a strong population of the spherical excited 0⁺ state. (author)