Underlying symmetries of realistic interactions and the nuclear many-body problem

Abstract

The present study brings forward important information, within the framework of spectral distribution theory, about the types of forces that dominate three realistic interactions, CD-Bonn, CD-Bonn+3terms, and GXPF1, in nuclei and their ability to account for many-particle effects such as the formation of correlated nucleon pairs and enhanced quadrupole collective modes. Like-particle and proton-neutron isovector pairing correlations are described microscopically by a model interaction with $\mathfrak{s}\mathfrak{p}$(4) dynamical symmetry, which is extended to include an additional quadrupole-quadrupole interaction. The analysis of the results for the $1{f}_{7/2}$ level shows that both CD-Bonn+3terms and GXPF1 exhibit a well-developed pairing character compared to CD-Bonn, while the latter appears to build up more (less) rotational isovector $T=1$ (isoscalar $T=0$) collective features. Furthermore, the three realistic interactions are in general found to correlate strongly with the pairing+quadrupole model interaction, especially for the highest possible isospin group of states where the model interaction can be used to provide a reasonable description of the corresponding energy spectra.