Final Report Summary - SDDCNS (Static and Dynamical Description of Correlated Nuclear Systems)
The main aim of the present Fellowship has been to investigate the properties of nuclear systems from first principles. The Fellow has followed three basic directions of research, summarized below.
DYNAMICAL CORRELATIONS IN REACTIONS
The dynamics of nuclear reactions have been studied using Green's functions techniques. As model systems, 1D collisions of nuclei have been analyzed. These provide a testing ground for future numerical codes in higher dimensions, while reproducing schematically the gross properties of central collisions. The major focus has been to understand the properties of time-evolving nuclear Green's functions, in particular off-diagonal elements in real space representation. For elements associated with distances over a few femtometers, these represent entanglement between far-away participants. At the late stages of a nuclear reaction, such matrix elements should not be entangled. Their influence on the dynamics of the system has been found to be negligibly small. Within the mean-field picture, the Fellow has also worked on implementing the evolution on a rotated coordinate frame that immediately averages out any off-diagonality via the coarseness of the mesh. This results in substantial improvements at the numerical level, supporting the extension to 2D and 3D nuclear systems. Finally, collisions have been studied beyond the mean-field approximation by fully implementing the Kadanoff-Baym equations within a second-order correlated approximation. Correlations affect substantially the thermalization time and the time evolution of collisions, providing additional friction that tends to damp out collective modes.
STATIC CORRELATIONS IN ISOSPIN ASYMMETRIC SYSTEMS
Studying nuclear matter within different many-body approaches, the Fellow has assessed various questions of interest for isospin asymmetric systems (systems with a different number of neutrons and protons). A connection has been established between a microscopic description of nuclear matter and the constraints arising from bulk properties in nuclear experiments. In particular, the density dependence of the symmetry energy has been determined microscopically, indicating that microscopic predictions reproduce well the previously well-known phenomenological tendencies.
In an effort to bring fully microscopic calculations closer to experimental data, the Fellow has developed a new approach to compute the nucleon mean-free path in the medium. The mean-free path relates directly to the absorption properties of the medium and its calculation provides a direct way to test the bulk component of the imaginary part of optical potentials. The approach is based on an extension of Green's functions into the complex plane and generalizes previously used approximations.
HOT NUCLEAR MATTER
During this 2-year span, the Fellow has developed a new project which aims at providing a microscopic description of the thermal properties of nuclear systems. To this end, the liquid-gas phase transition of nuclear matter has been studied within a self-consistent mean-field approximation. Analyzing the mean-field dependence of the phase transition, unexpected correlations arise between seemingly different properties. Similarly, correlations existing in oversimplified models can be immediately ruled out. The study of the critical exponents has confirmed, for the first time, the mean-field nature of the transition when studied within a self-consistent Hartree-Fock approximation. These results should provide a benchmark for theoretical advances in the study of multifragmentation reactions, where the liquid-gas transition is probed experimentally.
Continuing with this line of research, the Fellow has looked at the latent heat of the phase transition. Finally, the Fellow has secured his future research career by obtaining an Advanced Fellowship of the Science and Technology Facilities Council. This will provide further support for five years of research
DYNAMICAL CORRELATIONS IN REACTIONS
The dynamics of nuclear reactions have been studied using Green's functions techniques. As model systems, 1D collisions of nuclei have been analyzed. These provide a testing ground for future numerical codes in higher dimensions, while reproducing schematically the gross properties of central collisions. The major focus has been to understand the properties of time-evolving nuclear Green's functions, in particular off-diagonal elements in real space representation. For elements associated with distances over a few femtometers, these represent entanglement between far-away participants. At the late stages of a nuclear reaction, such matrix elements should not be entangled. Their influence on the dynamics of the system has been found to be negligibly small. Within the mean-field picture, the Fellow has also worked on implementing the evolution on a rotated coordinate frame that immediately averages out any off-diagonality via the coarseness of the mesh. This results in substantial improvements at the numerical level, supporting the extension to 2D and 3D nuclear systems. Finally, collisions have been studied beyond the mean-field approximation by fully implementing the Kadanoff-Baym equations within a second-order correlated approximation. Correlations affect substantially the thermalization time and the time evolution of collisions, providing additional friction that tends to damp out collective modes.
STATIC CORRELATIONS IN ISOSPIN ASYMMETRIC SYSTEMS
Studying nuclear matter within different many-body approaches, the Fellow has assessed various questions of interest for isospin asymmetric systems (systems with a different number of neutrons and protons). A connection has been established between a microscopic description of nuclear matter and the constraints arising from bulk properties in nuclear experiments. In particular, the density dependence of the symmetry energy has been determined microscopically, indicating that microscopic predictions reproduce well the previously well-known phenomenological tendencies.
In an effort to bring fully microscopic calculations closer to experimental data, the Fellow has developed a new approach to compute the nucleon mean-free path in the medium. The mean-free path relates directly to the absorption properties of the medium and its calculation provides a direct way to test the bulk component of the imaginary part of optical potentials. The approach is based on an extension of Green's functions into the complex plane and generalizes previously used approximations.
HOT NUCLEAR MATTER
During this 2-year span, the Fellow has developed a new project which aims at providing a microscopic description of the thermal properties of nuclear systems. To this end, the liquid-gas phase transition of nuclear matter has been studied within a self-consistent mean-field approximation. Analyzing the mean-field dependence of the phase transition, unexpected correlations arise between seemingly different properties. Similarly, correlations existing in oversimplified models can be immediately ruled out. The study of the critical exponents has confirmed, for the first time, the mean-field nature of the transition when studied within a self-consistent Hartree-Fock approximation. These results should provide a benchmark for theoretical advances in the study of multifragmentation reactions, where the liquid-gas transition is probed experimentally.
Continuing with this line of research, the Fellow has looked at the latent heat of the phase transition. Finally, the Fellow has secured his future research career by obtaining an Advanced Fellowship of the Science and Technology Facilities Council. This will provide further support for five years of research