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

Nuclear effective forces and isotope shifts

Signatures of criticality in the evolution of the nuclear ground-state shapes across the NxZ plane are discussed. Attention is paid to specific data indicating sudden structural changes in various isotopic and isotonic chains of medium-mass and heavy even-even nuclei, as well as to diverse theoretical aspects of the models used to describe these changes. The interacting boson model and the geometric collective model, in particular, are discussed in detail, the former providing global predictions for the evolution of collective observables in nuclei between closed shells and the latter yielding a parameter-efficient description of nuclei at the critical points of shape transitions. Some issues related to the mechanism of first- and second-order quantum phase transitions in general many-body systems are also outlined.

Quantum phase transitions in the shapes of atomic nuclei

Coexistence in even-mass nuclei

Laser spectroscopy for nuclear structure physics

Hyperfine structures and isotope shifts of strontium isotopes with A=78 to A=98 and A=100 were measured by collinear fast beam laser spectroscopy. Nuclear spins, moments and changes in mean square charge radii are extracted from the data. The spins and moments of most of the odd isotopes are explained in the framework of the single particle model. The changes in mean square charge radii are compared with predictions of the droplet model and of Hartree-Fock-plus-BCS calculations. For the isotopes in the transitional regions below and above the N=50 shell closure, the inclusion of quadrupole zero point motion in the Droplet model describes part of the observed shell effect. An additional change in the surface region of the charge distribution at spherical shape is suggested by the microscopic model. Furthermore, we propose that the isotopes $^{78}\mathrm{Sr}$ and $^{80}\mathrm{Sr}$ may show an unusual shape-sharing structure, with different mean deformations in the ground and ${2}_{1}^{+}$ excited states.

Systematics of nuclear ground state properties in Sr 78 – 100 by laser spectroscopy

Isotope shifts of the stable strontium isotopes $^{84}\mathrm{Sr}$, $^{86}\mathrm{Sr}$, $^{87}\mathrm{Sr}$, and $^{88}\mathrm{Sr}$ and the radioactive isotopes $^{89}\mathrm{Sr}$ and $^{90}\mathrm{Sr}$ have been measured using laser spectroscopy on collimated atomic beams. The changes in mean square charge radii extracted from the isotope shifts show a pronounced shell effect at the closed neutron shell N=50. The experimental data are compared with the predictions of the droplet model and Hartree-Fock plus BCS calculations. The analysis suggests that the changes in mean square charge radii are due to a change in size, a change in the predominantly dynamic deformation, and a change in the diffuseness of the nuclear charge distribution.

Influence of the N=50 shell closure on mean square charge radii of strontium

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Erratum: Systematics of nuclear ground state properties in 78-100 Sr by laser spectroscopy [Phys. Rev. C 41, 2883 (1990)]

The chain of Sr isotopes ranges from the neutron-shell closure at N = 50 into both the N = 38 and N = 60 deformation regions which represent the main topic of this workshop. For a detailed understanding of the nature of these nuclei, laser spectroscopy can provide the ground state spins and moments, as well as the the changes in the mean square charge radii as a function of the neutron number N. Recent experiments at Karlsruhe [1] and at Daresbury [2] essentially cover the neutron-deficient and stable Sr isotopes between N = 40 and N = 50. In order to complement these results, and to extend the measurements into the region of neutron-rich isotopes, we have performed an experiment at the ISOLDE isotope separator facility at CERN.

E. B. Ramsay

Papers

Systematics of nuclear ground state properties in Sr 78 – 100 by laser spectroscopy

Influence of the N=50 shell closure on mean square charge radii of strontium

Erratum: Systematics of nuclear ground state properties in 78-100 Sr by laser spectroscopy [Phys. Rev. C 41, 2883 (1990)]

Moments and Radii of 78–100Sr