Statistical Properties of Fermionic Molecular Dynamics

Statistical properties of Fermionic Molecular Dynamics are studied. It is shown that, although the centroids of the single--particle wave--packets follow classical trajectories in the case of a harmonic oscillator potential, the equilibrium properties of the system are the quantum mechanical ones. A system of weakly interacting fermions as well as of distinguishable particles is found to be ergodic and the time--averaged occupation probabilities approach the quantum canonical ones of Fermi--Dirac and Boltzmann statistics, respectively.Comment: 16 pages, several postscript figures, uses 'epsfig.sty'. More information is available at http://www.gsi.de/~schnack/fmd.htm

Fermionic Molecular Dynamics

A quantum molecular model for fermions is investigated which works with antisymmetrized many-body states composed of localized single-particle wave packets. The application to the description of atomic nuclei and collisions between them shows that the model is capable to address a rich variety of observed phenomena. Among them are shell effects, cluster structure and intrinsic deformation in ground states of nuclei as well as fusion, incomplete fusion, dissipative binary collisions and multifragmentation in reactions depending on impact parameter and beam energy. Thermodynamic properties studied with long time simulations proof that the model obeys Fermi-Dirac statistics and time averaging is equivalent to ensemble averaging. A first order liquid-gas phase transition is observed at a boiling temperature of $T \approx 5 MeV$ for finite nuclei of mass $16...40$.Comment: 61 pages, several postscript figures, uses 'epsfig.sty'. Report to be published in Prog. Part. Nucl. Phys. 39. More information available at http://www.gsi.de/~schnack/fmd.htm

Nuclear Structure based on Correlated Realistic Nucleon-Nucleon Potentials

We present a novel scheme for nuclear structure calculations based on realistic nucleon-nucleon potentials. The essential ingredient is the explicit treatment of the dominant interaction-induced correlations by means of the Unitary Correlation Operator Method (UCOM). Short-range central and tensor correlations are imprinted into simple, uncorrelated many-body states through a state-independent unitary transformation. Applying the unitary transformation to the realistic Hamiltonian leads to a correlated, low-momentum interaction, well suited for all kinds of many-body models, e.g., Hartree-Fock or shell-model. We employ the correlated interaction, supplemented by a phenomenological correction to account for genuine three-body forces, in the framework of variational calculations with antisymmetrised Gaussian trial states (Fermionic Molecular Dynamics). Ground state properties of nuclei up to mass numbers A<~60 are discussed. Binding energies, charge radii, and charge distributions are in good agreement with experimental data. We perform angular momentum projections of the intrinsically deformed variational states to extract rotational spectra.Comment: 32 pages, 15 figure

Multifragmentation calculated with relativistic force

A saturating hamiltonian is presented in a relativistically covariant formalism. The interaction is described by scalar and vector mesons, with coupling strengths adjusted to the nuclear matter. No explicit density depe ndence is assumed. The hamiltonian is applied in a QMD calculation to determine the fragment distribution in O + Br collision at different energies (50 -- 200 MeV/u) to test the applicability of the model at low energies. The results are compared with experiment and with previous non-relativistic calculations. PACS: 25.70Mn, 25.75.+rComment: 23 pages, latex, with 10 PS figures, available at http://www.gsi.de/~papp

Cluster structures within Fermionic Molecular Dynamics

The many-body states in an extended Fermionic Molecular Dynamics approach are flexible enough to allow the description of nuclei with shell model nature as well as nuclei with cluster and halo structures. Different many-body configurations are obtained by minimizing the energy under constraints on collective variables like radius, dipole, quadrupole and octupole deformations. In the sense of the Generator Coordinate Method we perform variation after projection and multiconfiguration calculations. The same effective interaction derived from realistic interactions by means of the Unitary Correlation Operator Method is used for all nuclei. Aspects of the shell model and cluster nature of the ground and excited states of C12 are discussed. To understand energies and radii of neutron-rich He isotopes the soft-dipole mode is found to be important.Comment: 5 pages, proceedings of the 8th International conference on Clustering Aspects of Nuclear Structure and Dynamics, Nov. 2003, Nara, Japan, to be published in Nucl. Phys.

Nucleon-nucleon potentials in phase-space representation

A phase-space representation of nuclear interactions, which depends on the distance $\vec{r}$ and relative momentum $\vec{p}$ of the nucleons, is presented. A method is developed that permits to extract the interaction $V(\vec{r},\vec{p})$ from antisymmetrized matrix elements given in a spherical basis with angular momentum quantum numbers, either in momentum or coordinate space representation. This representation visualizes in an intuitive way the non-local behavior introduced by cutoffs in momentum space or renormalization procedures that are used to adapt the interaction to low momentum many-body Hilbert spaces, as done in the unitary correlation operator method or with the similarity renormalization group. It allows to develop intuition about the various interactions and illustrates how the softened interactions reduce the short-range repulsion in favor of non-locality or momentum dependence while keeping the scattering phase shifts invariant. It also reveals that these effective interactions can have undesired complicated momentum dependencies at momenta around and above the Fermi momentum. Properties, similarities and differences of the phase-space representations of the Argonne and the N3LO chiral potential, and their UCOM and SRG derivatives are discussed

From nucleon-nucleon interaction matrix elements in momentum space to an operator representation

Starting from the matrix elements of the nucleon-nucleon interaction in momentum space we present a method to derive an operator representation with a minimal set of operators that is required to provide an optimal description of the partial waves with low angular momentum. As a first application we use this method to obtain an operator representation for the Argonne potential transformed by means of the unitary correlation operator method and discuss the necessity of including momentum dependent operators. The resulting operator representation leads to the same results as the original momentum space matrix elements when applied to the two-nucleon system and various light nuclei. For applications in fermionic and antisymmetrized molecular dynamics, where an operator representation of a soft but realistic effective interaction is indispensable, a simplified version using a reduced set of operators is given

The nuclear liquid-gas phase transition within Fermionic Molecular Dynamics

The time evolution of excited nuclei, which are in equilibrium with the surrounding vapour, is investigated. It is shown that the finite nuclear systems undergo a first oder phase transition. The caloric curve is presented for excited Oxygen, Magnesium, Aluminum and Calcium and the critical temperature is estimated for Oxygen.Comment: 8 pages, 3 postscript figures, uses 'epsfig.sty'. Submitted to Phys. Lett. B. More information available at http://www.gsi.de/~schnack/fmd.htm