Hartree-Fock Calculations with Skyrme's Interaction. I. Spherical Nuclei
TL;DR: In this article, Hartree-Fock equations for spherical nuclei using Skyrme's density-dependent effective nucleon-nucleon interaction are discussed systematically and the general formula for the mean energy of a spherical nucleus derived.
Abstract: Hartree-Fock calculations for spherical nuclei using Skyrme's density-dependent effective nucleon-nucleon interaction are discussed systematically. Skyrme's interaction is described and the general formula for the mean energy of a spherical nucleus derived. Hartree-Fock equations are obtained by varying the mean energy with respect to the single-particle wave functions of occupied states. Relations between the parameters of the Skyrme force and various general properties of nuclear matter and finite nuclei are analyzed. Calculations have been made for closed-shell nuclei using two rather different sets of parameters, both of which give good binding energies and radii for $^{16}\mathrm{O}$ and $^{208}\mathrm{Pb}$. Both interactions give good binding energies and charge radii for all closed-shell nuclei. Calculated electron scattering angular distributions agree qualitatively with experiment, and for one interaction there is good quantitative agreement. The single-particle energies calculated with the two interactions are somewhat different owing to a different nonlocality of the Hartree-Fock potentials, but both interactions give the correct order and density of single-particle levels near the Fermi level. They differ most strongly in their predictions for the energies of $1s$ single-particle states.
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TL;DR: In this paper, the authors review the present status of self-consistent mean field (SCMF) models for describing nuclear structure and low-energy dynamics and present several extensions beyond the mean-field model which are currently used.
Abstract: The authors review the present status of self-consistent mean-field (SCMF) models for describing nuclear structure and low-energy dynamics. These models are presented as effective energy-density functionals. The three most widely used variants of SCMF's based on a Skyrme energy functional, a Gogny force, and a relativistic mean-field Lagrangian are considered side by side. The crucial role of the treatment of pairing correlations is pointed out in each case. The authors discuss other related nuclear structure models and present several extensions beyond the mean-field model which are currently used. Phenomenological adjustment of the model parameters is discussed in detail. The performance quality of the SCMF model is demonstrated for a broad range of typical applications.
1,822 citations
TL;DR: In this article, the Lanczos tridiagonal construction has been used to diagonalize matrices in determinantal spaces of dimensionality up to 10^9 using the Shell Model.
Abstract: The last decade has witnessed both quantitative and qualitative progresses in Shell Model studies, which have resulted in remarkable gains in our understanding of the structure of the nucleus. Indeed, it is now possible to diagonalize matrices in determinantal spaces of dimensionality up to 10^9 using the Lanczos tridiagonal construction, whose formal and numerical aspects we will analyze. Besides, many new approximation methods have been developed in order to overcome the dimensionality limitations. Furthermore, new effective nucleon-nucleon interactions have been constructed that contain both two and three-body contributions. The former are derived from realistic potentials (i.e., consistent with two nucleon data). The latter incorporate the pure monopole terms necessary to correct the bad saturation and shell-formation properties of the realistic two-body forces. This combination appears to solve a number of hitherto puzzling problems. In the present review we will concentrate on those results which illustrate the global features of the approach: the universality of the effective interaction and the capacity of the Shell Model to describe simultaneously all the manifestations of the nuclear dynamics either of single particle or collective nature. We will also treat in some detail the problems associated with rotational motion, the origin of quenching of the Gamow Teller transitions, the double beta-decays, the effect of isospin non conserving nuclear forces, and the specificities of the very neutron rich nuclei. Many other calculations--that appear to have ``merely'' spectroscopic interest--are touched upon briefly, although we are fully aware that much of the credibility of the Shell Model rests on them.
884 citations
TL;DR: In this article, the atomic mass excesses and binding energies, ground-state shell-plus-pairing corrections, ground state microscopic corrections, and nuclear ground state deformations of 9318 nuclei ranging from 16O to A = 339 were tabulated.
802 citations
TL;DR: A review of the state-of-the-art in the field can be found in this paper, where the authors present a brief summary of the one- or multidimensional spherical or non-spherical explosion simulations available to date.
706 citations
TL;DR: The relativistic mean field model of the nucleus is reviewed in this article, where the meson fields are treated as mean fields, i.e. as nonquantal c-number fields, and the effect of the Dirac sea of the nucleons is neglected.
Abstract: The relativistic mean-field model of the nucleus is reviewed. It describes the nucleus as a system of Dirac nucleons which interact in a relativistic covariant manner via meson fields. The meson fields are treated as mean fields, i.e. as non-quantal c-number fields. The effect of the Dirac sea of the nucleons is neglected. The model is interpreted as a phenomenological ansatz providing a self-consistent relativistic description of nuclei and nuclear dynamics. It is viewed, so to say, as the relativistic generalisation of the Skyrme-Hartree-Fock ansatz. The capability and the limitations of the model to describe nuclear properties are discussed. Recent applications to spherical and deformed nuclei and to nuclear dynamics are presented.
704 citations