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We derive large-amplitude collective equations of motion from the variational principle for the time-dependent Schroedinger equation. These equations reduce to the well-known diabatic formulas for vibrational frequencies in the small amplitude limit. The finite amplitude expression allows departures from harmonic behavior of giant resonances to be simply estimated. The relative shift of the second phonon falls with nuclear mass A as A^(-4/3) in the three modes we consider: monopole, dipole, a...
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 ...
The influence of s- and p-wave interactions on trapped degenerate one and two-component Fermi gases is investigated. The energy functional of a multicomponent Fermi gas is derived within the Thomas-Fermi approximation including the s- and p-wave terms of an effective contact interaction. On this basis the stability of the dilute gas against mean-field induced collapse due to attractive interactions is investigated and explicit stability conditions in terms of Fermi momentum and s- and p-wave ...
The stability of trapped dilute Fermi gases against collapse towards large densities is studied. A hermitian effective contact-interaction for all partial waves is derived, which is particularly suited for a mean-field description of these systems. Including the s- and p-wave parts explicit stability conditions and critical particle numbers are given as function of the scattering lengths. The p-wave contribution determines the stability of a single-component gas and can substantially modify t...
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 multif...
The time-dependent variational principle for many-body trial states is used to discuss the relation between the approaches of different molecular dynamics models to describe indistinguishable fermions. Early attempts to include effects of the Pauli principle by means of nonlocal potentials as well as more recent models which work with antisymmetrized many-body states are reviewed under these premises. Keywords: Many-body theory; Fermion system; Molecular dynamics; Wave-packet dynamics; Time-d...
The structure and stability of dilute degenerate Fermi gases trapped in an external potential is discussed with special emphasis on the influence of s- and p-wave interactions. In a first step an Effective Contact Interaction for all partial waves is derived, which reproduces the energy spectrum of the full potential within a mean-field model space. Using the s- and p-wave part the energy density of the multi-component Fermi gas is calculated in Thomas-Fermi approximation. On this basis the s...
The Unitary Correlation Operator Method (UCOM) is employed to treat short-range correlations in both, homogeneous liquid and small droplets of bosonic He-4 atoms. The dominating short-range correlations in these systems are described by an unitary transformation in the two-body relative coordinate, applied either to the many-body state or to the Hamiltonian and other operators. It is shown that the two-body correlated interaction can describe the binding energy of clusters of up to 6 atoms ve...