Mean field theory

This book describes recent theoretical and experimental developments in the study of static and dynamic properties of atomic nuclei, many-body systems of strongly interacting neutrons and protons. The theoretical approach is based on the concept of the mean field, describing the motion of a nucleon in terms of a self-consistent single-particle potential well which approximates the interactions of a nucleon with all the other nucleons. The theoretical approaches also go beyond the mean-field approximation by including the effects of two-body collisions. The self-consistent mean-field approximation is derived using the effective nucleon-nucleon Skyrme-type interaction. The many-body problem is described next in terms of the Wigner phase space of the one-body density, which provides a basis for semi-classical approximations and leads to kinetic equations. Results of static properties of nuclei and properties associated with small amplitude dynamics are also presented. Relaxation processes, due to nucleon-nucleon collisions, are discussed next, followed by instability and large amplitude motion of excited nuclei. Lastly, the book ends with the dynamics of hot nuclei. The concepts and methods developed in this book can be used for describing properties of other many-body systems.

Intro -- Contents -- Preface -- Introduction -- 1. Self-consistent mean field approximations -- 1.1 Variational principle -- 1.2 Effective interparticle interaction -- 1.2.1 Nuclear matter -- 1.2.2 Finite nuclei -- 1.2.3 Landau's effective interaction -- 1.3 Energy density functional -- 1.3.1 Potential energy due to Skyrme forces -- 1.3.2 Spin-orbit potential energy -- 1.3.3 Coulomb energy -- 1.3.4 Energy density -- 1.4 Hartree-Fock equations for Skyrme forces -- 1.4.1 Nuclear matter properties in terms of Skyrme force parameters

1.4.2 Skyrme parameters in terms of nuclear matter properties -- 1.4.3 Determining the Skyrme force parameters -- 2. Many-body problem in phase space -- 2.1 Weyl's and Wigner's representations -- 2.1.1 Weyl representation -- 2.1.2 Wigner representation -- 2.1.3 Composition formula -- 2.2 Wigner distribution function -- 2.3 Application of the Wigner transformation -- 2.3.1 Kinetic equations -- 2.3.2 Pauli blocking -- 2.3.3 Heavy-ion collisions -- 2.4 Energy weighted smearing -- 2.5 Temperature smearing -- 2.6 Semi-classical approximation -- 2.7 Density of internal kinetic energy

2.8 Grand canonical potential density -- 3. Fluid dynamics approach -- 3.1 W…