The effective interaction of two nucleons in the s-d shell

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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“…(55). Two such iterative schemes were derived by Lee and Suzuki [61]. We will focus on the folded diagram method of Kuo and co-workers [15].…”

Section: Folded Diagrams and The Effective Valence Space Interactionmentioning

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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“…Furthermore, even the same defining equation for Ω can be solved by different iterative schemes. As an example one often employs the ansatz by Lee and Suzuki [2,3] for the wave operator…”

Section: One-flavor Channelmentioning

confidence: 99%

Convergence of multi-channel effective interactions

et al. 2006

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A detailed analysis of convergence properties of the Andreozzi-Lee-Suzuki iteration method, which is used for the calculation of low-momentum effective potentials V low k is presented. After summarizing different modifications of the iteration method for one-flavor channel we introduce a simple model in order to study the generalization of the iteration method to multi-flavor channels. The failure of a straightforward generalization is discussed. The introduction of a channel-dependent cutoff cures the conceptual and technical problems. This novel method has already been applied successfully for realistic hyperon-nucleon interactions.

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“…In practice the V low-k interaction can be derived either using model space methods (such as Lee-Suzuki [21] or Okubo [22]) or through an renormalization group treatment [20]. Both approaches are essentially equivalent and lead to the same energy-independent potential [23].…”

Section: Model Of the Nn Interactionmentioning

confidence: 99%

“…By introducing a cutoff Λ in momentum space, one separates the Hilbert space into a low-momentum and a high-momentum part. The renormalization technique (see, e.g., [20][21][22][23][24]) determines an effective Hamiltonian, which must be diagonalized within the model space (below the cutoff). With the cutoff in the range of Λ = 2 fm −1 V low-k becomes model independent, and reproduces the deuteron binding energy, low-energy phase shifts, and half-on-shell T matrix with the same accuracy as the initial realistic interaction.…”

Section: Introductionmentioning

confidence: 99%

Separable form of a low-momentum realisticNNinteraction

et al. 2010

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The low-momentum interaction V low-k derived from realistic models of the nucleon-nucleon interaction is presented in a separable form. This separable force is supported by a contact interaction in order to achieve the saturation properties of symmetric nuclear matter. Bulk properties of nuclear matter and finite nuclei are investigated for the separable form of V low-k and two different parameterizations of the contact term. The accuracy of the separable force in Hartree-Fock calculations with respect to the original interaction V low-k is discussed. For a cutoff parameter Λ of 2 fm −1 a representation by a rank 2 separable force yields a sufficient accuracy, while higher ranks are required for larger cut-off parameters. The resulting separable force is parameterized in a simple way to allow for an easy application in other nuclear structure calculations.

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The effective interaction of two nucleons in the s-d shell

Cited by 115 publications

References 13 publications

Effective interactions and the nuclear shell-model

Effective interactions and the nuclear shell-model

Convergence of multi-channel effective interactions

Separable form of a low-momentum realisticNNinteraction

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