Influence of saturation properties on shell-model calculations

Abzouzi, A.; Caurier, E.; Zuker, A. P.

doi:10.1103/physrevlett.66.1134

Cited by 44 publications

(54 citation statements)

References 20 publications

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“…all the way down to agreement with experiment. However more detailed analysis of the results close to 116 Sn indicates that our effective two-particle interaction has difficulties in reproducing the shell closure which is believed to occur in this region. The increase of the the 0 + − 2 + splitting is not as sharp as found experimentally, even if the phenomenon is rather weak in the case of Sn.…”

Section: Tin Isotopes For 100 ≤ a ≤ 132mentioning

confidence: 93%

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Effective interactions and the nuclear shell-model

Dean

Engeland

Hjorth‐Jensen

et al. 2004

Progress in Particle and Nuclear Physics

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This review aims at a critical discussion of the interplay between effective interactions derived from various manybody approaches and spectroscopic data extracted from large scale shell-model studies. To achieve this, our many-body scheme starts with the free nucleon-nucleon (NN) interaction, typically modelled on various meson exchanges. The NN interaction is in turn renormalized in order to derive an effective medium dependent interaction. The latter is in turn used in shell-model calculations of selected nuclei. We also describe how to sum up the parquet class of diagrams and present initial uses of the effective interactions in coupled cluster many-body theory.

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Section: Tin Isotopes For 100 ≤ a ≤ 132mentioning

confidence: 93%

“…Then the diagonalization process in Eqs. (116)(117)) is repeated and a new iteration to the true eigenvectors is obtained.…”

Section: New Correction Vectors Are Calculated Through the Stepsmentioning

confidence: 99%

Effective interactions and the nuclear shell-model

Dean

Engeland

Hjorth‐Jensen

et al. 2004

Progress in Particle and Nuclear Physics

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“…It has been demonstrated in Refs. [1,7] that one may obtain a reliable multipole Hamiltonian from G-matrix, but the monopole Hamiltonian is often incorrect. However, the monopole Hamiltonian has large influence on the large-scale shell model calculations because of the significant role at shell structure evolution [1].…”

Section: Introductionmentioning

confidence: 99%

Systematic study of shell-model effective interaction insdshell

Wang

Dong

Fang

2014

EPJ Web of Conferences

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Abstract.The spin-tensor decomposition method has been used to analyze the shell model effective interactions in sd shell systematically. Almost all the interactions have been studied, including the microscopic interactions and phenomenological ones. It can be noticed that the discrepancies between the central force of microscopic interactions with the ones of empirical interactions are remarkable.

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“…This is not a joke, but an important remark: NO provides the foundation for a conventional G-matrix study. As emphasized over the years [10,23,25], the realistic Gmatrices are very close to one another and will provide good spectra once monopole corrected. Absolute energies term through a uniform attraction of 1.5 MeV (in CK it is about 3 times as large).…”

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confidence: 99%

Three-Body Monopole Corrections to Realistic Interactions

2003

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It is shown that a very simple three-body monopole term can solve practically all the spectroscopic problems-in the p, sd and pf shells-that were hitherto assumed to need drastic revisions of the realistic potentials.PACS numbers: 21.60. Cs, 21.30.+y, The first exact Green's function Monte Carlo (GFMC) solutions for A > 4 nuclei confirmed that two-body (2b) interactions fell short of perfectly reproducing experimental data [1]. The inclusion of a three-body (3b) force lead to excellent spectroscopy, but some problems remained for the binding and symmetry energies and spin orbit splittings. No core shell model calculations (NCSM) [2] have recently developped to the point of approximating the exact solutions with sufficient accuracy to provide a very important-though apparently negative-result in 10 B [3]: While in the lighter systems the spectra given by a strict two-body potential are not always good-but always acceptable-in 10 B, the spectrum is simply very bad.My purpose is to show the striking analogy between this situation and what occurs in conventional (0 ω) shell model calculations with realistic G-matrices, and then explain how a very simple 3b term can solve practically all the spectroscopic problems-in the p, sd and pf shells-that were hitherto assumed to need drastic revisions of the realistic (R) 2b potentials.The first realistic matrix elements [5], and the first large scale shell model codes [6] appeared almost simultaneously. Calculations for up to five particles in the sd shell gave very satisfactory results, but the spectrum of 22 Na (i.e., (sd) 6 T = 0) was very bad [7]. (Note that 10 B is (p) 6 T = 0). At the time nobody thought of 3b forces, and naturally the blame was put on the 2b matrix elements (V JT stuv , stuv are subshells). The proposed phenomenological cures amounted to fit them to the experimental levels. Two "schools" emerged: One proposed to fit them all (63 in the sd shell), and lead eventually to the famous USD interaction [8,9]. The alternative was to fit only the centroids, given in Eqs. (1,2).They are associated to the 2b quadratics in number (n s ) and isospin operators (T s ), Eqs. (3,4), and they define the monopole Hamiltonian, Eq. (5), in which we have added the single particle (1b) term. The idea originated in Ref.[10], where it was found that the Kuo Brown (KB) interaction in the pf shell [11] could yield excellent spectroscopy through the modificationsThe validity of this prescription was checked in perturbative calculations [12], and convincingly confirmed for A = 47 − 52 once exact diagonalizations became feasible [13,14,15,16, 17].In what follows f will stand generically for (p 3/2 , d 5/2 , f 7/2 ) in the (p, sd, pf ) shells respectively. Obviously r = p 1/2 and r ≡ d 3/2 , s 1/2 for the p and sd shells.Nowadays the 2b N N potentials are nearly perfect, and the calculations are exact. Therefore, the blame for bad spectroscopy must be put on the absence of 3b terms. Which means that the monopole corrections must be 3b and Eq. (5) must be supplemented bywhere n stu ...

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Influence of saturation properties on shell-model calculations

Cited by 44 publications

References 20 publications

Effective interactions and the nuclear shell-model

Effective interactions and the nuclear shell-model

Systematic study of shell-model effective interaction insdshell

Three-Body Monopole Corrections to Realistic Interactions

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