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

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

Mean-field instability of trapped dilute boson-fermion mixtures

The influence of boson-boson and boson-fermion interactions on the stability of a binary mixture of bosonic and fermionic atoms is investigated. The density profiles of the trapped mixture are obtained from direct numerical solution of a modified Gross-Pitaevskii equation that is self-consistently coupled to the mean-field generated by the interaction with the fermionic species. The fermions which in turn feel the mean-field created by the bosons are treated in Thomas-Fermi approximation. We study the effects of different combinations of signs of the boson-boson and the boson-fermion scattering lengths and determine explicit expressions for critical particle numbers as function of these scattering lengths.Comment: 4 pages, 2 figures (using RevTeX4

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.

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

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

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