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

Table of experimental nuclear ground state charge radii: An update

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.

The shell model as a unified view of nuclear structure

Energy levels of light nuclei A=8,9,10

The available data on nuclear fusion cross sections important to energy generation in the Sun and other hydrogen-burning stars and to solar neutrino production are summarized and critically evaluated. Recommended values and uncertainties are provided for key cross sections, and a recommended spectrum is given for {sup 8}B solar neutrinos. Opportunities for further increasing the precision of key rates are also discussed, including new facilities, new experimental techniques, and improvements in theory. This review, which summarizes the conclusions of a workshop held at the Institute for Nuclear Theory, Seattle, in January 2009, is intended as a 10-year update and supplement to 1998, Rev. Mod. Phys. 70, 1265.

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Solar fusion cross sections II: the pp chain and CNO cycles

Radioactive atoms produced in proton-induced nuclear reactions and released from thick targets have been ionized resonantly by laser radiation in a hot tube connected to the target container. Pulsed tuneable lasers with a repetition rate as high as 10 kHz have been applied for stepwise resonant excitation and photoionization in the last step. In this way the efficiency and selectivity of the target and ion source system which serves as an injector to the on-line isotope separators at CERN-ISOLDE could be improved. In a series of off-line and on-line studies the ionization of Sn ( E i = 7.3 eV), Tm ( E i = 6.2 eV), Yb ( E i = 6.2 eV) and Li ( E i = 5.4 eV) was investigated. An ionization efficiency of up to 15% was obtained for Yb. The ratio of the laser-ionized and surface-ionized ion currents was measured as a function of temperature for different ionization cavity materials (W, Ta, Nb and TaC). It was shown that this ratio, i.e. the selectivity, rises for Tm from 10 to 10000 with falling temperature and is strongly dependent on the material. Since the lasers are pulsed the ion beam becomes bunched with a pulse width of about 10–50 μs. This width is strongly dependent on the potential drop along the tube (caused by the electric current used for heating the tube) and on the alignment of the laser beams with respect to the tube axis. The selectivity could be further improved by a factor of 10 using gated detection of the bunched ion beam.

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Chemically selective laser ion-source for the CERN-ISOLDE on-line mass separator facility

The use of chemically selective laser ionization combined with $\ensuremath{\beta}$-delayed neutron counting at CERN/ISOLDE has permitted identification and half-life measurements for 623-ms ${}^{61}\mathrm{Mn}$ up through 14-ms ${}^{69}\mathrm{Mn}$. The measured half-lives are found to be significantly longer near $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}40$ than the values calculated with a quasiparticle random-phase-approximation shell model. Gamma-ray singles and coincidence spectroscopy has been performed for ${}^{64,66}\mathrm{Mn}$ decays to levels of ${}^{64,66}\mathrm{Fe}$, revealing a significant drop in the energy of the first ${2}^{+}$ state in these nuclides that suggests an unanticipated increase in collectivity near $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}40$.

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Decay of Neutron-Rich Mn Nuclides and Deformation of Heavy Fe Isotopes

At the ISOLDE on line mass separator a system of copper vapor lasers and dye lasers serves for resonant ionization of atoms inside a hot cavity attached to the target. Radioactive ion beams of Yb, Ag, Mn, Ni, Zn, Be, Cu, Cd and Sn were produced with the Resonance Ionization Laser Ion Source (RILIS). Two and three step excitation schemes are used, providing an ionization efficiency of about 10%. Thanks to the use of the RILIS it became possible to ionize beryllium efficiently at ISOLDE, and all particle stable Be isotopes could be separated for the first time. Separation of Ag and Cu nuclear isomers was achieved in the ion source by appropriate tuning of the laser wavelength. New isotopes of Ag, Mn, Zn, Cd and Sn were found, including the r process “waiting point” nucleus 129Ag.

The ISOLDE laser ion source for exotic nuclei

The applications of the laser resonance ionization method in nuclear research are reviewed. Investigation of radioactive isotopes using resonance ionization techniques provides a valuable combination of high selectivity, efficiency and spectral resolution. The majority of radioactive ion beams produced at on-line isotope separator facilities profit from the selectivity and universal applicability of laser ion sources. Numerous ultra-sensitive and high-resolution techniques of laser spectroscopy based on resonance ionization of atoms have been developed for the study of rare and radioactive isotopes. A summary of ionization schemes applied to radioactive isotopes is given in table form.

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Resonance laser ionization of atoms for nuclear physics

The magnetic moment of ${}^{11}\mathrm{Be}$ ( ${T}_{1/2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}13.8\phantom{\rule{0ex}{0ex}}\mathrm{s}$) was measured by detecting nuclear magnetic resonance signals in a beryllium crystal lattice. The experimental technique applied to a ${}^{11}{\mathrm{Be}}^{+}$ ion beam from a laser ion source includes in-beam optical polarization, implantation into a metallic single crystal, and observation of rf resonances in the asymmetric angular distribution of the $\ensuremath{\beta}$ decay ( $\ensuremath{\beta}$-NMR). The nuclear magnetic moment $\ensuremath{\mu}{(}^{11}\mathrm{Be})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1.6816(8)\phantom{\rule{0ex}{0ex}}{\ensuremath{\mu}}_{N}$ provides a stringent test for theoretical models describing the structure of the $1/{2}^{+}$ neutron halo state.

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V. I. Mishin

Papers

Chemically selective laser ion-source for the CERN-ISOLDE on-line mass separator facility

Decay of Neutron-Rich Mn Nuclides and Deformation of Heavy Fe Isotopes

The ISOLDE laser ion source for exotic nuclei

Resonance laser ionization of atoms for nuclear physics

Measurement of the Magnetic Moment of the One-Neutron Halo Nucleus B 11 e