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

Random-matrix theories in quantum physics : common concepts

Annals of physics

We review the development of random-matrix theory (RMT) during the last decade. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the localization problem, many-body quantum systems, the Calogero-Sutherland model, chiral symmetry breaking in QCD, and quantum gravity in two dimensions. The review is preceded by a brief historical survey of the developments of RMT and of localization theory since their inception. We emphasize the concepts common to the above-mentioned fields as well as the great diversity of RMT. In view of the universality of RMT, we suggest that the current development signals the emergence of a new "statistical mechanics": Stochasticity and general symmetry requirements lead to universal laws not based on dynamical principles.

Random Matrix Theories in Quantum Physics: Common Concepts

THE subject of quantum electrodynamics is extremely difficult, even for the case of a single electron. The usual method of solving the corresponding wave equation leads to divergent integrals. To avoid these, Prof. P. A. M. Dirac* uses the method of redundant variables. This does not abolish the difficulty, but presents it in a new form, which may be dealt with in two ways. The first of these needs only comparatively simple mathematics and is directly connected with an elegant general scheme, but unfortunately its wave functions apply only to a hypothetical world and so its physical interpretation is indirect. The second way has the advantage of a direct physical interpretation, but the mathematics is so complicated that it has not yet been solved even for what appears to be the simplest possible case. Both methods seem worth further study, failing the discovery of a third which would combine the advantages of both.

http://ieeexplore.ieee.org/iel5/3/22993/01069961.pdf

Quantum electrodynamics

This paper reviews various results related to the single-particle structure in spherical and deformed nuclei, discussed from the viewpoint of the so-called shell-correction method. This method stresses the importance of large-scale nonuniformities in the energy distribution of the individual particles especially near the Fermi energy. The way in which these nonuniformities affect in an essential way many nuclear properties, such as the shape stiffness, the spatial density distribution, the total mass of the nucleus, the mass and inertia of the nuclear shape variations, etc. is also discussed. Against this background, the behavior of the nuclear deformation energy is described, in particular for larger distortions relevant to the fission process. In this connection, some qualitative singularities of the phenomenological liquid-drop deformation energy at large shape distortions are pointed out, and their possible implications for fission are discussed. As the problems considered cover a wide range of nuclear properties, this paper is not a review in the narrow sense of the word. Comparison with other approaches as well as historic references are given mainly to clarify specific points, because a complete review would be a monumental undertaking.

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Funny Hills: The Shell-Correction Approach to Nuclear Shell Effects and Its Applications to the Fission Process

Simple expressions are obtained for the total reaction cross section in terms of the interaction barrier for the $s$ wave. These expressions allow the interaction barrier to be determined experimentally. Analysis of experimental data for heavy ions on $^{238}\mathrm{U}$ shows that the effective radius parameter decreases as projectile charges increase.

Interaction Barrier in Charged-Particle Nuclear Reactions

Nucleon-nucleon collisions nucleus-nucleus collisions properties of quark-gluon plasma production and experimental search for quark-gluon plasma.

Introduction to High-Energy Heavy-Ion Collisions

We explore molecular states of two open heavy-quark mesons $(Q\overline{q})\ensuremath{-}(q\overline{Q})$ in a quark-based model in terms of a four-body nonrelativistic Hamiltonian with pairwise effective interactions. Molecular states are found in the combinations of ${D,{D}^{*},B,{B}^{*}}$ with ${\overline{D},{\overline{D}}^{*},\overline{B},{\overline{B}}^{*}}$, including a weakly bound $D{\overline{D}}^{*}$ state near the threshold which may be qualitatively identified as the 3872 state observed recently by the Belle Collaboration.

Molecular states of heavy quark mesons

Using the color-singlet free energy ${F}_{1}$ and total internal energy ${U}_{1}$ obtained by Kaczmarek et al. (hep-lat/0309121) for a static quark Q and an antiquark $\overline{Q}$ in quenched QCD, we study the binding energies and wave functions of heavy quarkonia in a quark-gluon plasma. By minimizing the grand potential in a simplified schematic model, we find that the proper color-singlet $Q\text{\ensuremath{-}}\overline{Q}$ potential can be obtained from the total internal energy ${U}_{1}$ by subtracting the gluon internal energy contributions. We carry out this subtraction in the local energy-density approximation in which the gluon energy density can be related to the local gluon pressure by the quark-gluon plasma equation of state. We find in this approximation that the proper color-singlet $Q\text{\ensuremath{-}}\overline{Q}$ potential is approximately ${F}_{1}$ for $T~{T}_{c}$ and it changes to $\frac{3}{4}{F}_{1}+\frac{1}{4}{U}_{1}$ at high temperatures. In this potential model, the $J/\ensuremath{\psi}$ is weakly bound above the phase-transition temperature ${T}_{c}$, and it dissociates spontaneously above $1.62{T}_{c}$, whereas ${\ensuremath{\chi}}_{c}$ and ${\ensuremath{\psi}}^{'}$ are unbound in the quark-gluon plasma. The bottomium states $\ensuremath{\Upsilon},{\ensuremath{\chi}}_{b}$, and ${\ensuremath{\Upsilon}}^{'}$ are bound in the quark-gluon plasma and they dissociate at $4.1{T}_{c},1.18{T}_{c},$ and $1.38{T}_{c}$ respectively. For comparison, we evaluate the heavy quarkonium binding energies also in other models using the free energy ${F}_{1}$ or the total internal energy ${U}_{1}$ as the $Q\text{\ensuremath{-}}\overline{Q}$ potential. The comparison shows that the model with the new $Q\text{\ensuremath{-}}\overline{Q}$ potential proposed here gives dissociation temperatures that agree best with those from spectral function analyses. We evaluate the cross section for $\ensuremath{\sigma}(g+J/\ensuremath{\psi}\ensuremath{\rightarrow}c+\overline{c})$ and its inverse process to determine the $J/\ensuremath{\psi}$ dissociation width and the rate of $J/\ensuremath{\psi}$ production by recombining c and $\overline{c}$ in the quark-gluon plasma.

Cheuk-Yin Wong

Papers

Funny Hills: The Shell-Correction Approach to Nuclear Shell Effects and Its Applications to the Fission Process

Interaction Barrier in Charged-Particle Nuclear Reactions

Introduction to High-Energy Heavy-Ion Collisions

Molecular states of heavy quark mesons

Heavy quarkonia in quark-gluon plasma