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, CDBonn+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 Sp(4) dynamical symmetry, which is extended to include an additional quadrupole-quadrupole interaction. The analysis of the results for the 1f 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.

Global properties of fp-shell interactions in many-nucleon systems

“…In comparison, the CD-Bonn+3terms interaction in the 1f 7/2 orbit exhibits well-developed pairing and rotational characteristics [18]. Such a difference in the behavior of CD-Bonn+3terms within both regions, 1f 7/2 and upper fp, may reflect the fact that this interaction was determined through a reproduction of the low-lying energy spectrum and binding energy of A = 48 1f 7/2 nuclei.…”

“…The most general model interaction with Sp(4) dynamical symmetry [17] has been found to provide for a reasonable microscopic description of the pairing-governed isobaric analog 0 + states in light and medium mass nuclei and to account quite well for the observed detailed structure beyond mean-field effects such as the N = Z anomalies, isovector pairing gaps and staggering effects [16]. In addition, the H sp(4) interaction (4) has been shown to strongly correlate, especially when the quadrupole term is introduced, with the "CD-Bonn", CD-Bonn+3terms and GXPF1 interactions in the 1f 7/2 orbit [18].…”

“…We have already illustrated such an example and its significance by exploration of the 1f 7/2 orbit [18]. Individual orbit analyses render correlation coefficients that are free of the influence of any one-body interaction [by definition, (Appendix Eq.…”

“…In this respect, correlation coefficients can be used to extract information how well pairing/rotational features are developed in interactions, which may differ substantially from an individual comparison of pairing/quadrupole interaction strengths [18]. (2) It gives an exact prescription for identifying the pure zero-(centroid), oneand two-body parts of an interaction under a given space partitioning.…”

Generalized seniority for the shell model with realistic interactions

“…Alternatively, since the generalized seniority approach is based upon the dominance of pairing correlations, it is worth investigating the possibility that the decomposition of realistic interactions into pairing and non-pairing (e.g., quadrupole) components through the use of spectral distribution theory, as carried out in Ref. [41], could yield relevant measures.…”