  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.
