Staggering behavior of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mn>0</mml:mn><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math>state energies in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mtext>Sp</mml:mtext><mml:mo>(</mml:mo><mml:mn>4</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>pairing model

Sviratcheva, K. D.; Georgieva, A. I.; Draayer, J. P.

doi:10.1103/physrevc.69.024313

Cited by 13 publications

(6 citation statements)

References 60 publications

(131 reference statements)

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“…However, for the T z = 0 case of ee and oo nuclei the primary contribution of the residual interaction is from the symmetry energy. We also note that since pp, nn, and pn T = 1 pairs coexist [57,60,61], Stg…”

Section: Stgmentioning

confidence: 71%

“…We utilize the formulae of Ref. [57], some of which are provided here for completeness, and follow the analysis reported in there. The discrete approximations of the E 0 energy are given as…”

Section: Discrete Derivatives and Fine Structure Effectsmentioning

confidence: 99%

“…As suggested in Refs. [27,[57][58][59], the significance of various energy filters can be understood using phenomenological arguments that can be given a simple and useful graphical representation. Specifically, in the following subsections, each nucleus is represented by an inactive part, or a general ee or oo nucleus, schematically illustrated by a box, , in which the interaction between the constituent particles does not change for a given energy filter.…”

Section: Discrete Derivatives and Fine Structure Effectsmentioning

confidence: 99%

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Exact isovector pairing in a shell-model framework: Role of proton-neutron correlations in isobaric analog states

et al. 2019

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We utilize a nuclear shell model Hamiltonian with only two adjustable parameters to generate, for the first time, exact solutions for pairing correlations for light to medium-mass nuclei, including the challenging proton-neutron pairs, while also identifying the primary physics involved. In addition to single-particle energy and Coulomb potential terms, the shell model Hamiltonian consists of an isovector T = 1 pairing interaction and an average proton-neutron isoscalar T = 0 interaction, where the T = 0 term describes the average interaction between non-paired protons and neutrons. This Hamiltonian is exactly solvable, where, utilizing 3 to 7 single-particle energy levels, we reproduce experimental data for 0 + state energies for isotopes with mass A = 10 through A = 62 exceptionally well including isotopes from He to Ge. Additionally, we isolate effects due to like-particle and protonneutron pairing, provide estimates for the total and proton-neutron pairing gaps, and reproduce N (neutron) = Z (proton) irregularity. These results provide a further understanding for the key role of proton-neutron pairing correlations in nuclei, which is especially important for waiting-point nuclei on the rp-path of nucleosynthesis.

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Section: Stgmentioning

confidence: 71%

Section: Discrete Derivatives and Fine Structure Effectsmentioning

confidence: 99%

Section: Discrete Derivatives and Fine Structure Effectsmentioning

confidence: 99%

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Exact isovector pairing in a shell-model framework: Role of proton-neutron correlations in isobaric analog states

et al. 2019

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“…Similar type of correlation effects, based on coupling of identical nucleons, were then suggested by Bohr, Mottelson and Pines [232] to explain the energy gap observed in the spectra of even-even nuclei and the concept was soon after applied by Belyaev in the first detailed (mean-field) study of pairing in nuclei in terms of independent quasi-particles [233]. Along with approximate mean field solutions (for a review see, e.g., [234]), the pairing problem was approached by various group theoretical methods, e.g., the like-pair SU(2) seniority model (see, e.g., [222,235]), the SO(5)/Sp(4) model for isovector (pp,pn, and nn) pairing (see, e.g., [236][237][238][239][240]), and the SO(8) model with the additional isoscalar pn channel (see, e.g., [241,242]). We note that the notation of Sp(4) corresponds to a notation of Sp(6, R) for the symplectic scheme of Sec.…”

Section: Seniority Scheme and Exact Pairing Theorymentioning

confidence: 99%

Symmetry-guided large-scale shell-model theory

Launey

Dytrych

Draayer

2016

Progress in Particle and Nuclear Physics

131

173

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In this review, we present a symmetry-guided strategy that utilizes exact as well as partial symmetries for enabling a deeper understanding of and advancing ab initio studies for determining the microscopic structure of atomic nuclei. These symmetries expose physically relevant degrees of freedom that, for large-scale calculations with QCD-inspired interactions, allow the model space size to be reduced through a very structured selection of the basis states to physically relevant subspaces. This can guide explorations of simple patterns in nuclei and how they emerge from first principles, as well as extensions of the theory beyond current limitations toward heavier nuclei and larger model spaces. This is illustrated for the ab initio symmetry-adapted no-core shell model (SA-NCSM) and two significant underlying symmetries, the symplectic Sp(3, R) group and its deformation-related SU(3) subgroup. We review the broad scope of nuclei, where these symmetries have been found to play a key role -from the light p-shell systems, such as 6 Li, 8 B, 8 Be, 12 C, and 16 O, and sd-shell nuclei exemplified by 20 Ne, based on first-principle explorations; through the Hoyle state in 12 C and enhanced collectivity in intermediate-mass nuclei, within a no-core shell-model perspective; up to strongly deformed species of the rare-earth and actinide regions, as investigated in earlier studies. A complementary picture, driven by symmetries dual to Sp(3, R), is also discussed. We briefly review symmetry-guided techniques that prove useful in various nuclear-theory models, such as Elliott model, ab initio SA-NCSM, symplectic model, pseudo-SU(3) and pseudo-symplectic models, ab initio hyperspherical harmonics method, ab initio lattice effective field theory, exact pairing -plusshell model approaches, and cluster models, including the resonating-group method. Important implications of these approaches that have deepened our understanding of emergent phenomena in nuclei, such as enhanced collectivity, giant resonances, pairing, halo, and clustering, are discussed, with a focus on emergent patterns in the framework of the ab initio SA-NCSM with no a priori assumptions.

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“…The pn pairing also plays a signiˇcant role in reproducing the experimental data for the S 2p two-proton separation energy around Z = N [9]. The zero point of S 2p determines the two-proton-drip line, which according to the Sp (4) [9] reveal additional features of the nuclear interaction and provide for a good test of the model.…”

Section: The Application Of the Sp(4) Dynamical Symmetry To Pairing Cmentioning

confidence: 80%

Dynamical symmetries in contemporary nuclear structure applications

et al. 2010

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In terms of group theory Å the language of symmetries, the concept of spontaneous symmetry breaking is represented in terms of chains of groupÄsubgroup structures that deˇne the dynamical symmetry of the system under consideration. This framework enables exact analytic solutions of the associated eigenvalue problems.We review two types of applications of dynamical symmetries in contemporary theoretical nuclear structure physics:ˇrst for a classiˇcation of the many-body systems under consideration, with respect to an important characteristic of their behavior; and second for the creation of exactly solvable algebraic models that describe speciˇc aspects of this behavior. This is illustrated with the boson and fermion realizations of symplectic structures; in theˇrst case with an application of the sp(4, R) classiˇcation scheme of evenÄeven nuclei within the major nuclear shells and next with an application of the sp(4) microscopic model for the description of isovector pairing correlations.

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Staggering behavior of0+state energies in theSp(4)pairing model

Cited by 13 publications

References 60 publications

Exact isovector pairing in a shell-model framework: Role of proton-neutron correlations in isobaric analog states

Exact isovector pairing in a shell-model framework: Role of proton-neutron correlations in isobaric analog states

Symmetry-guided large-scale shell-model theory

Dynamical symmetries in contemporary nuclear structure applications

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