Two-neutron transfer reactions as a tool to study the interplay between shape coexistence and quantum phase transitions

The atomic mass table presents zones where the structure of the states changes rapidly as a function of the neutron or proton number.Among them,notable examples are the A≈100 Zr region,the Pb region around the neutron midshell(N=104),and the N≈90 rare-earth region.The observed phenomena can be understood in terms of either shape coexistence or quantum phase transitions.The objective of this study is to find an observable that can distinguish between both shape coexistence and quantum phase transitions.As an observable to be analyzed,we selected the two-neutron transfer intensity between the 0+states in the parent and daughter nuclei.The framework used for this study is the Interacting Boson Model(IBM),including its version with configuration mixing(IBM-CM).To generate wave functions of isotope chains of interest needed for calculating transfer intensities,previous systematic studies using IBM and IBM-CM were used without changing the parameters.The results of two-neutron transfer intensities are presented for Zr,Hg,and Pt isotopic chains using IBM-CM.Moreover,for Zr,Pt,and Sm isotopic chains,the results are presented using IBM with only a single configuration,i.e.,without using configuration mixing.For Zr,the two-neutron transfer intensities between the ground states provide a clear observable,indicating that normal and intruder configurations coexist in the low-lying spectrum and cross at A=98→100.This can help clarify whether shape coexistence induces a given quantum phase transition.For Pt,in which shape coexistence is present and the regular and intruder configurations cross for the ground state,there is almost no impact on the value of the two-neutron transfer intensity.Similar is the situation with Hg,where the ground state always has a regular nature.For the Sm isotope chain,which is one of the quantum phase transition paradigms,the value of the two-neutron transfer intensity is affected strongly.