  In a recent paper (S. Ait El Korchi et al. 2020 EPL 132 52001), we explored,
inside the context of Critical Point Symmetries (CPSs) X(3) and Z(4), a
correlation between two exceedingly known quantum concepts, the Minimal Length
(ML) and the Deformation-Dependent Mass (DDM), that are commonly applied in
various areas of physics. Such a correlation has been strongly identified in
transition nuclei by calculating some physical observables of that quantum
system, like as energy spectra, moments of inertia and transition
probabilities. In this paper we extend that study to E(5) dynamical symmetry
corresponding to the shape phase transition U(5)$\leftrightarrow$O(6). The
experimental realization of the models was found to occur in some nuclei, using
the existing phenomenological potentials : Infinite Square Well, Davidson and
Kratzer, whose models fits provide the best agreement. Importantly the
calculations performed in this work using these potentials corroborate the fact
that the revealed correlation between both quantum concepts is not
destructively affected by the presence of other model parameters and hence its
existence is independent of the form or type of the used potential.
Undoubtedly, the present work will open the way for more investigations of this
correlation in the limits of other critical points symmetries in nuclear shape
phase transitions which play today a major role in nuclear structure research
from theoretical as well as experimental point of view.
