Marek Płoszajczak - Böcker

This book provides the first graduate-level, self-contained introduction to recent developments that lead to the formulation of the configuration-interaction approach for open quantum systems, the Gamow shell model, which provides a unitary description of quantum many-body system in different regimes of binding, and enables the unification in the description of nuclear structure and reactions. The Gamow shell model extends and generalizes the phenomenologically successful nuclear shell model to the domain of weakly-bound near-threshold states and resonances, offering a systematic tool to understand and categorize data on nuclear spectra, moments, collective excitations, particle and electromagnetic decays, clustering, elastic and inelastic scattering cross sections, and radiative capture cross sections of interest to astrophysics. The approach is of interest beyond nuclear physics and based on general properties of quasi-stationary solutions of the Schrödinger equation – so-called Gamow states. For the benefit of graduate students and newcomers to the field, the quantum-mechanical fundamentals are introduced in some detail. The text also provides a historical overview of how the field has evolved from the early days of the nuclear shell model to recent experimental developments, in both nuclear physics and related fields, supporting the unified description. The text contains many worked examples and several numerical codes are introduced to allow the reader to test different aspects of the continuum shell model discussed in the book.

Nuclei in their ground states behave as quantum fluids, Fermi liquids. When the density, or the temperature of that fluid increases, various phase transitions may occur. Thus, for moderate excitation energies, of the order of a few MeV per nucleon, nuclear matter behaves as an ordinary fluid with gaseous and liquid phases, and a coexistence region below a critical temperature. For higher excitation energies, of the order of a few Ge V per nucleon, the composition of nuclear matter changes, nucleons being gradually turned into baryonic resonances of various kinds. Finally, when 3 the energy density exceeds some few GeV /fm , nuclear matter turns into a gas of weakly interacting quarks and gluons. This new phase of matter has been called the quark-gluon plasma, and its existence is a prediction of Quantum Chromodynamics. Collisions of heavy ions produce nuclear matter with various degrees of excitation. In fact, by selecting the impact parameter and the bombarding energy, one can produce nuclear matter with specified baryonic density and excitation energy. Several major experimental programs are under way (for instance at GANIL, with the detector INDRA, at GSI with the detector ALADIN, at the CERN-SPS, at the AGS of Brookhaven, etc. ), or are in preparation (RRIC, LHC, etc. ). The goal of these experiments is to get evidence for the different phases of nuclear matter predicted by the theory, and to study their properties.

The main purpose of this book is to present, in a comprehensive and progressive way, the appearance of universal limit probability laws in physics, and their connection with the recently developed scaling theory of fluctuations. Arising from the probability theory and renormalization group methods, this novel approach has been proved recently to provide efficient investigative tools for the collective features that occur in any finite system.The mathematical background is self-contained and is formulated in terms which are easy to apply to the physical context. After illustrating the problem of anomalous diffusion, the book reviews recent advances in nuclear and high energy physics, where the limit laws are now recognized as being able to classify different phases of a system undergoing the pseudo-critical behaviour. A new description of the hadronic matter in terms of the fluctuation scaling is appearing as a consequence of this approach.