Fifty Years of the Shell Model — The Quest for the Effective Interaction

Talmi, Igal

doi:10.1007/0-306-47916-8_1

Cited by 30 publications

(37 citation statements)

References 267 publications

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“…10 isotopes. In semimagic spherical open-shell nuclei, the 2 + states lie at nearly constant energies along isotopic chains due to pairing correlations [64]. In our calculations, all isotopes from 42 Ca to 58 Ca exhibit this characteristic behavior because the insufficient spin-orbit splitting of the 0f levels creates a major shell with 20 < N ≤ 40.…”

Section: Frommentioning

confidence: 77%

Quasiparticle random-phase approximation with interactions from the Similarity Renormalization Group

Hergert

Papakonstantinou²,

Roth³

2011

Phys. Rev. C

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We have developed a fully consistent framework for calculations in the Quasiparticle Random Phase Approximation (QRPA) with N N interactions from the Similarity Renormalization Group (SRG) and other unitary transformations of realistic interactions. The consistency of our calculations, which use the same Hamiltonian to determine the Hartree-Fock-Bogoliubov (HFB) ground states and the residual interaction for QRPA, guarantees an excellent decoupling of spurious strength, without the need for empirical corrections. While work is under way to include SRGevolved 3N interactions, we presently account for some 3N effects by means of a linearly densitydependent interaction, whose strength is adjusted to reproduce the charge radii of closed-shell nuclei across the whole nuclear chart. As a first application, we perform a survey of the monopole, dipole, and quadrupole response of the calcium isotopic chain and of the underlying single-particle spectra, focusing on how their properties depend on the SRG parameter λ. Unrealistic spin-orbit splittings suggest that spin-orbit terms from the 3N interaction are called for. Nevertheless, our general findings are comparable to results from phenomenological QRPA calculations using Skyrme or Gogny energy density functionals. Potentially interesting phenomena related to low-lying strength warrant more systematic investigations in the future.

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Section: Frommentioning

confidence: 77%

Quasiparticle random-phase approximation with interactions from the Similarity Renormalization Group

Hergert

Papakonstantinou²,

Roth³

2011

Phys. Rev. C

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“…For over sixty years the nuclear shell-model approach has remained one of the most powerful theoretical tools available in studies of nuclear many-body problems [12][13][14]. The ability of the multi-configuration shell model (SM) to obtain level spectra and multiple other observables for a broad range of nuclear spectra using a single Hamiltonian, though be it somewhat phenomenological, gives this approach a practical advantage.…”

Section: Introductionmentioning

confidence: 99%

Nuclear clustering using a modern shell model approach

Volya

Tchuvil’sky

2015

Phys. Rev. C

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Nuclear clustering, alpha decays, and multi-particle correlations are important components of nuclear dynamics. In this work we put forward the Cluster-Nucleon Configuration Interaction Model. We use the modern configuration-interaction approach with advanced realistic shell-model Hamiltonians in order to study clustering phenomena; the study is facilitated by the algebraic properties of many-nucleon configurations in the harmonic oscillator basis.Using translationally invariant formalism we built cluster channels that satisfy Pauli exclusion principle as well as orthogonality and normalization conditions. We formally justify the formalism and demonstrate that, within the new method, clustering strengths satisfy sum rules that are consistent with the statistical properties of nuclear reactions with composite particles. Using properly renormalized cluster form factors our approach appears to resolve long-standing problems related to absolute normalization of the alpha clustering spectroscopic factors and their behavior in sd-shell nuclei.Our methods are demonstrated in studies of α spectroscopic factors in sd-shell nuclei and in 16 O treated in p-sd shells. Comparison with experimental data supports validity of the approach.

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“…The nuclear shell model is the basic model in nuclear physics [1][2][3][4][5][6][7][8][9][10]. The shell model describes nuclei by valence protons and valence neutrons outside a semi-or doubly magic core.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we investigate the simplest nuclei for which the shell model can be applied [7][8][9][10]. These are the nuclei which have one or two particles (holes) outside a doubly magic core with mass numbers A+δ, A+2δ, and A, respectively.…”

Section: Introductionmentioning

confidence: 99%

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Mass dependence of the surface δ-interaction strength for two-particle (two-hole) multiplets

Heusler

Brentano

2008

Eur. Phys. J. A

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Abstract. By using the surface δ-interaction, the lowest states in nuclei of atomic mass number 6 ≤ A ≤ 210 with a doubly magic core and two valence nucleons are investigated. A single parameter describes the strength of the multiplet splitting of the lowest configuration which includes the ground state. The dependence of the strength on the atomic mass number of the doubly magic core is determined as a power law function A −f with an exponent f =

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Fifty Years of the Shell Model — The Quest for the Effective Interaction

Cited by 30 publications

References 267 publications

Quasiparticle random-phase approximation with interactions from the Similarity Renormalization Group

Quasiparticle random-phase approximation with interactions from the Similarity Renormalization Group

Nuclear clustering using a modern shell model approach

Mass dependence of the surface δ-interaction strength for two-particle (two-hole) multiplets

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