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.

Self-consistent mean-field models for nuclear structure

Relativistic mean field theory in finite nuclei

RIPL – Reference Input Parameter Library for Calculation of Nuclear Reactions and Nuclear Data Evaluations

Adopted values for the reduced electric quadrupole transition probability, B(E2)↑, from the ground state to the first-excited 2+ state of even–even nuclides are given in Table I. Values of τ, the mean life of the 2+ state; E, the energy; and β, the quadrupole deformation parameter, are also listed there. The ratio of β to the value expected from the single-particle model is presented. The intrinsic quadrupole moment, Q0, is deduced from the B(E2)↑ value. The product E×B(E2)↑ is expressed as a percentage of the energy-weighted total and isoscalar E2 sum-rule strengths.

Table II presents the data on which Table I is based, namely the experimental results for B(E2)↑ values with quoted uncertainties. Information is also given on the quantity measured and the method used. The literature has been covered to November 2000.

The adopted B(E2)↑ values are compared in Table III with the values given by systematics and by various theoretical models. Predictions of unmeasured B(E2)↑ values are also given in Table III.

Transition probability from the ground to the first-excited 2^+ state of even-even nuclides

Annalen der Physik

Correlations beyond the mean field in magnesium isotopes: angular momentum projection and configuration mixing

Particle number projection with effective forces

The fission barriers of the nuclei ${}^{254}\mathrm{Fm},$ ${}^{256}\mathrm{Fm},$ ${}^{258}\mathrm{Fm},$ ${}^{258}\mathrm{No}$, and ${}^{260}\mathrm{Rf}$ are investigated in a fully microscopic way up to the scission point. The analysis is based on the constrained Hartree-Fock-Bogoliubov theory and Gogny's D1S force. The quadrupole, octupole, and hexadecapole moments as well as the number of nucleons in the neck region are used as constraints. Two fission paths, corresponding to the bimodal fission, are found. The decrease with isotope mass of the half-life times of heavy Fm isotopes is also explained.

/pdf/self-consistent-calculations-of-fission-barriers-in-the-fm-3evp2gxn7g.pdf

Self-consistent calculations of fission barriers in the Fm region

A systematic study of 160 heavy and superheavy nuclei is performed in the Hartree-Fock-Bogoliubov (HFB) approach with the finite-range and density-dependent Gogny force with the D1S parameter set. We show calculations in several approximations: with axially symmetric and reflection-symmetric wave functions, with axially symmetric and non-reflection-symmetric wave functions, and finally with some representative triaxial wave functions. Relevant properties of the ground state and along the fission path are thoroughly analyzed. Fission barriers, ${Q}_{\ensuremath{\alpha}}$ factors, and lifetimes with respect to fission and $\ensuremath{\alpha}$ decay as well as other observables are discussed. Larger configuration spaces and more general HFB wave functions as compared to previous studies provide a very good agreement with the experimental data.

/pdf/fission-half-lives-of-superheavy-nuclei-in-a-microscopic-21f6t3muls.pdf

Fission half-lives of superheavy nuclei in a microscopic approach

The collective yrast band of the nucleus ${}^{48}\mathrm{Cr}$ is studied using the spherical shell model and the Hartree-Fock-Bogoliubov (HFB) method. Both approaches produce basically the same axially symmetric intrinsic state up to the---accurately reproduced---observed backbending. Agreement between both calculations extends to most observables. The only significant discrepancy comes from the static moments of inertia and can be attributed to the need of a more refined treatment of pairing correlations in the HFB calculation.

J. L. Egido

Papers

Correlations beyond the mean field in magnesium isotopes: angular momentum projection and configuration mixing

Particle number projection with effective forces

Self-consistent calculations of fission barriers in the Fm region

Fission half-lives of superheavy nuclei in a microscopic approach

Intrinsic vs laboratory frame description of the deformed nucleus 48Cr.