  Realistic nucleon-nucleon (NN) interactions, derived within the framework of
meson theory or more recently in terms of chiral effective field theory, yield
new possibilities for achieving a unified microscopic description of atomic
nuclei. Based on spectral distribution methods, a comparison of these
interactions to a most general Sp(4) dynamically symmetric interaction, which
previously we found to reproduce well that part of the interaction that is
responsible for shaping pairing-governed isobaric analog 0+ states, can
determine the extent to which this significantly simpler model Hamiltonian can
be used to obtain an approximate, yet very good description of low-lying
nuclear structure. And furthermore, one can apply this model in situations that
would otherwise be prohibitive because of the size of the model space. In
addition, we introduce a Sp(4) symmetry breaking term by including the
quadrupole-quadrupole interaction in the analysis and examining the capacity of
this extended model interaction to imitate realistic interactions. This
provides a further step towards gaining a better understanding of the
underlying foundation of realistic interactions and their ability to reproduce
striking features of nuclei such as strong pairing correlations or collective
rotational motion.
