C. Bahri

Generalized pseudo-SU(3) model and pairing☆

The pseudo-SU(3) model is extended to explicitly include the spin and proton-neutron degrees of freedom. A general formalism for evaluating matrix elements of one-body and two-body tensor operators within this framework is presented. The pairing interaction, which couples different irreducible representations of SU(3), is expressed in terms of pseudo-space tensors and a general result is given for calculating its matrix elements. The importance of pairing correlations in pseudo-SU(3) model calculations is demonstrated by examining the dependence of wavefunctions, low-energy collective excitation spectra, and moments of inertia on the strength of the pairing interaction.Abstract The pseudo-SU(3) model is extended to explicitly include the spin and proton-neutron degrees of freedom. A general formalism for evaluating matrix elements of one-body and two-body tensor operators within this framework is presented. The pairing interaction, which couples different irreducible representations of SU(3), is expressed in terms of pseudo-space tensors and a general result is given for calculating its matrix elements. The importance of pairing correlations in pseudo-SU(3) model calculations is demonstrated by examining the dependence of wavefunctions, low-energy collective excitation spectra, and moments of inertia on the strength of the pairing interaction.

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 12C and 16O is reported. Eigenstates of 12C and 16O, determined within the framework of the no-core shell model using the J-matrix inverse scattering potential with A<or=16 (JISP16) nucleon-nucleon (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 Elliotts 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.

Ab initio symplectic no-core shell model

The no-core shell model (NCSM) is a prominent ab initio method that yields a good description of the low-lying states in few-nucleon systems as well as in more complex p-shell nuclei. Nevertheless, its applicability is limited by the rapid growth of the many-body basis with larger model spaces and increasing number of nucleons. The symplectic no-core shell model (Sp-NCSM) aspires to extend the scope of the NCSM beyond the p-shell region by augmenting the conventional spherical harmonic oscillator basis with the physically relevant symplectic symmetry-adapted configurations of the symplectic shell model that describe naturally the monopole?quadrupole vibrational and rotational modes, and also partially incorporate ?-cluster correlations. In this review, the models underpinning the Sp-NCSM approach, namely, the NCSM, the Elliott SU(3) model and the symplectic shell model, are discussed. Following this, a prescription for constructing translationally invariant symplectic configurations in the spherical harmonic oscillator basis is given. This prescription is utilized to unveil the extent to which symplectic configurations enter into low-lying states in 12C and 16O nuclei calculated within the framework of the NCSM with the JISP16 realistic nucleon?nucleon interaction. The outcomes of this proof-of-principle study are presented in detail.

Hoyle state and rotational features in Carbon-12 within a no-core shell model framework

Abstract By using only a fraction of the model space extended beyond current no-core shell-model limits and a many-nucleon interaction with a single parameter, we gain additional insight within a symmetry-guided shell-model framework, into the many-body dynamics that gives rise to the ground state rotational band together with phenomena tied to alpha-clustering substructures in the low-lying states in 12C, and in particular, the challenging Hoyle state and its first 2 + and 4 + excitations. For these states, we offer a novel perspective emerging out of no-core shell-model considerations, including a discussion of associated nuclear deformation and matter radii. This, in turn, provides guidance for ab initio shell models by informing key features of nuclear structure and the interaction.

SU(3) reduced matrix element package

A new SU(3) reduced matrix element package, which exploits logical operations and bit manipulation procedures in implementing a fermion second-quantized formulation for calculating matrix elements of SU(3)-coupled products of creation and annihilation operators (a†, a†a†, a, aa, a†a, a†a†a, a †aa, a†a†aa), is introduced. The reduced matrix elements are extracted from full matrix elements of the coupled operators. Since the reduced matrix elements do not depend on the subgroup chain, the evaluation is carried out in the SU(3) ⊃ SU(2) ⊗ U(1) basis as it is the simplest to use. The results can be extended to more complicated operator forms, either indirectly through the use of SU(3) and SU(2) recoupling procedures or directly by a straightforward extension of routines that are part of the current package.

Symplectic No-core Shell-model Approach to Intermediate-mass Nuclei

We present a microscopic description of nuclei in an intermediate-mass region, including the proximity to the proton drip line, based on a no-core shell model with a schematic many-nucleon long-range interaction with no parameter adjustments. The outcome confirms the essential role played by the symplectic symmetry to inform the interaction and the winnowing of shell-model spaces. We show that it is imperative that model spaces be expanded well beyond the current limits up through fifteen major shells to accommodate particle excitations that appear critical to highly-deformed spatial structures and the convergence of associated observables.

Monopole-pairing and deformation in atomic nuclei☆

Abstract The pairing-plus-qua upole model is realized in the framework of the Elliott SU(3) scheme in order to study the complementary and competing features of the pairing and quadrupole-quadrupole interactions. The pairing force is shown to break the SU(3) symmetry and — in conjunction with the quadrupole-quadrupole force — remove almost all degeneracies which occur in the pure symmetry limits of the theory. In addition, ground-state deformations induced by pairing are shown to be triaxial but rather soft, whereas the quadrupole-quadrupole interaction favors prolate or oblate shapes which are sharp.

Highly deformed modes in the ab initio symplectic no-core shell model

We show that highly deformed modes essential for nuclear dynamics modeling can readily be included in the symplectic no-core shell model (Sp-NCSM) space. In particular, a prescription for constructing general deformed k-particle–k-hole (kp–kh) translationally invariant symplectic starting state configurations and symplectic excitations thereof in a fermion-based spherical harmonic oscillator basis is presented. This prescription is used to build the symplectic excitations over all possible as well as the most deformed configurations in 12C and 16O. The extent to which these configurations enter into low-lying states for these nuclei calculated within the framework of the no-core shell model with a realistic microscopic interaction is then determined. Typically, the addition of these and representations to the leading results grow the overall overlap with the no-core-shell-model eigenstates by 5–10% for a total of 85–90%. And most importantly, even with the addition of these higher-order particle–hole configurations, the dimensionality of the symplectic subspace constitutes a very small fraction of the conventional full no-core shell model space, which reaffirms the relevance of the Sp-NCSM scheme.

Effects of pairing in the pseudo-SU(3) model

Abstract An extended version of the pseudo-SU(3) model which includes both spin and proton-neutron degrees of freedom is used to study the influence of the pairing interaction on K -band mixing, B (E2) values and quadrupole moments. Using the asymmetric rotor model as a backdrop, specific consequences of a many-particle shell-model based description of these collective properties are demonstrated and fundamental limits of the collective models approach are investigated. Finally, the pseudo-SU(3) model, including representation mixing induced by pairing, is used to calculate the energies of 140 Ce and the results are compared to experimental data and other theories.

Resonant modes in light nuclei

Abstract The microscopic character of the giant quadrupole resonance in light, deformed nuclei is explored within the context of the contracted sympletic model. Some results are given for 24Mg. A simple parameter, the quadrupole-quadrupole interaction strength, suffices to fix the location of the resonance, the strength of low-lying as well as high-lying 2 +→O g+ transitions, and the groundband deformation. The resonance is found to be a highly coherent excitation that spans more than a dozen major shells of the oscillator. Additionally, the results show that the giant resonance is just one manifestation of the existence of a strongly deformed band (βr≈1.5βg) in the continuum that mirrors the low-lying rotational structure.