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 N = 104 neutron midshell or the N ≈ 90 rare-earth region. The
observed phenomena can be understood in terms either of shape coexistence or quantum phase
transitions. The goal of this study is to find an observable that could distinguish between both
phenomena, shape coexistence and quantum phase transitions. The selected observable to be
analyzed is the two-neutron transfer intensity between the 0 + states in the parent and daughter
nuclei. The framework in which the study is done is the Interacting Boson Model (IBM), including
its version with configuration mixing (IBM-CM). In order to generate the wave functions of the
isotope chains of interest, needed for calculating transfer intensities, previous systematic studies
with IBM and IBM-CM are taken without changing the parameters. Results for two-neutron
transfer intensities are presented for Zr, Hg and Pt isotopic chains using IBM-CM and, moreover,
the same is done for Zr, Pt and Sm isotopic chains using IBM with just a single configuration, i.e.,
without using configuration mixing. In the case of 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 that they cross at A = 98 → 100, and this could allow to
disentangle whether or not shape coexistence is inducing a given QPT. In the case of Pt, where
shape coexistence is present and the regular and the intruder configurations cross for the ground
state, there is almost no influence in the value of the two-neutron transfer, neither in the case of
Hg where the ground state always has regular nature. For the Sm isotope chain that is one of the
quantum phase transition paradigms, the value of the two-neutron transfer is strongly affected.
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