K. D. Sviratcheva

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.

Racah’s method for general subalgebra chains: Coupling coefficients of SO(5) in canonical and physical bases

It is shown that the method of infinitesimal generators (“Racah’s method”) can be broadly and systematically formulated as a method applicable to the calculation of reduced coupling coefficients for a generic subalgebra chain G⊃H, provided the reduced matrix elements of the generators of G and the recoupling coefficients of H are known. The calculation of SO(5)⊃SO(4) reduced coupling coefficients is considered as an example, and a procedure for transformation of reduced coupling coefficients between canonical and physical subalegebra chains is presented. The problem of calculating coupling coefficients for generic irreps of SO(5), reduced with respect to any of its subalgebra chains, is completely resolved by this approach.

Deformations of the fermion realization of the sp(4) algebra and its subalgebras

With a view towards future applications in nuclear physics, the fermion realization of the compact symplectic sp(4) algebra and its q-deformed versions are investigated. Three important reduction chains of the sp(4) algebra are explored in both the classical and deformed cases. The deformed realizations are based on distinct deformations of the fermion creation and annihilation operators. For the primary reduction, the su(2) substructure can be interpreted as either the spin, isospin or angular momentum algebra, whereas for the other two reductions su(2) can be associated with pairing between fermions of the same type or pairing between two distinct fermion types. Each reduction provides for a complete classification of the basis states. The deformed induced u(2) representations are reducible in the action spaces of sp(4) and are decomposed into irreducible representations.

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.

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

Abstract 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 ℏ Ω 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 58Ni and 58Cu.

An algebraic pairing model with Sp(4) symmetry and its deformation

A fermion realization of the compact symplectic sp(4) algebra provides a natural framework for studying isovector-pairing correlations in nuclei. While these correlations manifest themselves most clearly in the binding energies of 0+ ground states, they also have a large effect on the energies of excited states, including especially excited 0+ states. In this paper, we consider non-deformed as well as deformed algebraic descriptions of pairing through the reductions of sp(q)(4) to different realizations of u(q)(2) for single-j and multi-j orbitals. The model yields a classification scheme for completely paired 0+ states of even–even and odd–odd nuclei in the 1d3/2, 1f7/2 and 1f5/2 2p1/2 2p3/2 1g9/2 shells. Phenomenological non-deformed and deformed isospin-breaking Hamiltonians are expressed in terms of the generators of the dynamical symmetry groups Sp(4) and Spq(4). These Hamiltonians are related to the most general microscopic pairing problem, including isovector pairing and isoscalar proton–neutron interaction along with nonlinear interaction in the deformed extension. In both the non-deformed and deformed cases the eigenvalues of the Hamiltonian are fit to the relevant Coulomb corrected experimental 0+ energies and this, in turn, allows us to estimate the interaction strength parameters, to investigate isovector-pairing properties and symmetries breaking and to predict the corresponding energies. While the non-deformed theory yields results that are comparable to other theories for light nuclei, the deformed extension, which takes into account higher order interactions between the particles, gives a better fit to the data. The multi-shell applications of the model provide for reasonable predictions of energies of exotic nuclei.

Staggering behavior of 0^+ state energies in the Sp(4) pairing model

We explore, within the framework of an algebraic sp(4) shell model, discrete approximations to various derivatives of the energies of the lowest isovector-paired 0^+ states of atomic nuclei in the 40 <A < 100 mass range. The results show that the symplectic model can be used to successfully interpret fine structure effects driven by the proton-neutron (pn) and like-particle isovector pairing interactions as well as interactions with higher J multipolarity. A finite energy difference technique is used to investigate two-proton and two-neutron separation energies, observed irregularities found around the N=Z region, and the like-particle and pn isovector pairing gaps. A prominent staggering behavior is observed between groups of even-even and odd-odd nuclides. An oscillation, in addition to that associated with changes in isospin values, that tracks with alternating seniority quantum numbers related to the isovector pairing interaction is also found.

q-Deformation of symplectic dynamical symmetries in algebraic models of nuclear structure

With a view toward further nuclear structure applications of approaches based on quantum-deformed (or q-deformed) algebras, introduced to the authors by Yu.F. Smirnov, we construct a q analog of a boson realization of the symplectic noncompact sp(4, R) algebra together with a q analog of a fermion realization of the symplectic compact sp(4) algebra. The first study, on the q-deformed Sp(4,R) symmetry, is applied to the development of a q analog of the two-dimensional Interacting Boson Model with q-deformed SU(3) the underpinning dynamical symmetry group. An explicit realization in terms of q-tensor operators with respect to the standard suq(2) algebra is given. The group-subgroup structure of this framework yields the physical interpretation of the generators of the groups under consideration. The second symplectic algebra, the q-deformed sp(4), is applied to studying isovector pairing correlations in atomic nuclei. A specific q deformation of the sp(4) algebra is realized in terms of q deformed fermion creation and annihilation operators of the shell model. The generators of the algebra close on four distinct realizations of the uq(2) subalgebra. These reductions, which correspond to different types of pairing interactions, yield a complete classification of the basis states. An analysis of the role of the q deformation is based on a comparison of the results for energies of the lowest isovector-paired 0+ states in the deformed and nondeformed cases.

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{sup +} states in light and medium-mass nuclei may mix with one another and reveals possible, but still extremely weak, nonanalog {beta}-decay transitions.