Dynamical Symmetries Reflected in Realistic Interactions

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.Comment: 10 pages, 4 figures, Proceedings of the XXV International Workshop on Nuclear Theory, June 26-July 1, 2006, Rila Mountains, Bulgari

Ab initio open core shell model for nuclear structure

The SU(3) symmetry-adapted version of the No-Core Shell Model (NCSM), which reduces to the Elliott SU(3) Model in its 0ω limit, is described and shown to be effective in providing an efficient description of low-lying eigenstates of 12C and 16O. A symmetry-guided framework is suggested based on our recent findings of low-spin and high-deformation dominance in realistic NCSM results. This holds promise to significantly enhance the reach of ab initio shell models. © 2010 IOP Publishing Ltd

Generalized q-Deformed Symplectic sp(4) Algebra for Multi-shell Applications

A multi-shell generalization of a fermion representation of the q-deformed compact symplectic sp_q(4) algebra is introduced. An analytic form for the action of two or more generators of the Sp_q(4) symmetry on the basis states is determined and the result used to derive formulae for the overlap between number preserving states as well as for matrix elements of a model Hamiltonian. A second-order operator in the generators of Sp_q(4) is identified that is diagonal in the basis set and that reduces to the Casimir invariant of the sp(4) algebra in the non-deformed limit of the theory. The results can be used in nuclear structure applications to calculate beta-decay transition probabilities and to provide for a description of pairing and higher-order interactions in systems with nucleons occupying more than a single-j orbital.Comment: 10 page

Isospin symmetry breaking in an algebraic pairing Sp(4) model

An exactly solvable sp(4) algebraic approach extends beyond the traditional isospin-conserving nuclear interaction to bring forward effects of isospin symmetry breaking and isospin mixing resulting from a two-body nuclear interaction that includes proton-neutron (pn) and like-particle isovector pairing correlations plus significant isoscalar pn interactions. The model yields an estimate for the extent to which isobaric analog 0+ states in light and medium-mass nuclei may mix with one another and reveals possible, but still extremely weak, nonanalog β-decay transitions. © 2005 The American Physical Society

Dynamical symmetry of isobaric analog 0\u3csup\u3e+\u3c/sup\u3e states in medium mass nuclei

An algebraic sp(4) shell model is introduced to achieve a deeper understanding and interpretation of the properties of pairing-governed 0 + states in medium mass atomic nuclei. The theory, which embodies the simplicity of a dynamical symmetry approach to nuclear structure, is shown to reproduce the excitation spectra and fine structure effects driven by proton-neutron interactions and isovector pairing correlations across a broad range of nuclei

Physical significance of q deformation and many-body interactions in nuclei

The pairing correlations in nuclie with mass 40 ≤ A ≤ 100 were studied. The study was carried out by using the concept of quantum deformation. It was observed that the q ≠ 1 was uniformly superior to those of the nondeformed limit and that the q parameter varies smoothly with nuclear characteristics. It was found that the q deformation plays a significant role in understanding higher-order effects in the many body interaction