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

Light Nuclei in the Framework of the Symplectic No-core Shell Model

A symplectic no-core shell model (Sp-NCSM) is constructed with the goal of extending the {\it ab-initio} NCSM to include strongly deformed higher-oscillator-shell configurations and to reach heavier nuclei that cannot be studied currently because the spaces encountered are too large to handle, even with the best of modern-day computers. This goal is achieved by integrating two powerful concepts: the {\it ab-initio} NCSM with that of the $\mathrm{Sp}(3,\mathbb{R})\supset\mathrm{SU}(3)$ group-theoretical approach. The NCSM uses modern realistic nuclear interactions in model spaces that consists of many-body configurations up to a given number of $\hbar\Omega$ excitations together with modern high-performance parallel computing techniques. The symplectic theory extends this picture by recognizing that when deformed configurations dominate, which they often do, the model space can be better selected so less relevant low-lying $\hbar\Omega$ configurations yield to more relevant high-lying $\hbar\Omega$ configurations, ones that respect a near symplectic symmetry found in the Hamiltonian. Results from an application of the Sp-NCSM to light nuclei are compared with those for the NCSM and with experiment.Comment: 9 pages, 3 figures, Proceedings of the XXV International Workshop on Nuclear Theory, June 26-July 1, 2006, Rila Mountains, Bulgari

Evidence for Symplectic Symmetry in Ab Initio No-Core Shell Model Results for Light Nuclei

Clear evidence for symplectic symmetry in low-lying states of $^{12}$C and $^{16}$O is reported. Eigenstates of $^{12}$C and $^{16}$O, determined within the framework of the no-core shell model using the JISP16 $NN$ realistic interaction, typically project at the 85-90% level onto a few of the most deformed symplectic basis states that span only a small fraction of the full model space. The results are nearly independent of whether the bare or renormalized effective interactions are used in the analysis. The outcome confirms Elliott's \SU{3} model which underpins the symplectic scheme, and above all, points to the relevance of a symplectic no-core shell model that can reproduce experimental B(E2) values without effective charges as well as deformed spatial modes associated with clustering phenomena in nuclei.Comment: 4 pages, 3 figures, to be published in Physics Review Letter

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

Global Properties of fp-Shell Interactions in Many-nucleon Systems

Spectral distribution theory, which can be used to compare microscopic interactions over a broad range of nuclei, is applied in an analysis of two modern effective interactions based on the realistic CD-Bonn potential for $0\hbar\Omega$ no-core shell model calculations in the fp shell, as well as in a comparison of these with the realistic shell-model GXPF1 interaction. In particular, we explore the ability of these interaction to account for the development of isovector pairing correlations and collective rotational motion in the fp shell. Our findings expose the similarities of these two-body interactions, especially as this relates to their pairing and rotational characteristics. Further, the GXPF1 interaction is used to determine the strength parameter of a quadrupole term that can be used to augment an isovector-pairing model interaction with Sp(4) dynamical symmetry, which in turn is shown to yield reasonable agreement with the low-lying energy spectra of $^{58}$Ni and $^{58}$Cu.Comment: 21 pages, 3 figures, accepted in Nuclear Physics

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