Title: The TDHF code Sky3D

A reduced Green's function formulation of time-dependent Hartree--Fock theory is developed using diagrammatic techniques. The resulting integral equations are transformed using a power moment approach. An asymptotic ansatz of the form exp)-(-2(epsilon/sub i/ minus-or-plus..omega..))/sup 1/2/r)amdagger polynomial is used to fit the radial functions phi/sup + -//sub l/(r). From these functions, the frequency-dependent dipole, quadrupole, and octapole polarizabilities of the helium isoelectronic sequence for Z=2--10 are calculated. Results are reported for the static case. It is found that the poles of the polarizabilities which correspond to TDHF excitation energies from the ground state can be accurately determined for highly excited states.more » These excitation energies are reported and are related to a Rydberg formula. The resulting quantum defects are also reported.« less

The nuclear fluid dynamical model with final thermal breakup is used to study the reactions {sup 20}Ne + {sup 238}U and {sup 40}Ar + {sup 40}Ca at E{sub LAB} = 390 MeV/n. The calculated double differential cross sections d{sup 2}{sigma}/d{Omega}dE are in agreement with recent experimental data. However, it is shown that the azimuthal dependence of the triple differential distributions d{sup 3}{sigma}/dEdcos{theta}d{phi}, to be obtained from 4{pi} exclusive experiments with single event analysis, can yield considerably deeper insight into the collision process and allow for snapshots of the reactions. Strongly correlated jets of nuclear matter are predicted.

A method for solving the TDHF-equation for the one-particle density matrix is suggested. The density matrix is expanded into Gaussian phase-space densities after a transformation to Wigner space. If the Hartree potential is approximated by a quadratic potential at the centers of the Gaussian density matrices, classical equations of motion are obtained for the phase-space coordinates of the centers. In addition, differential equations of first order have to be solved for the time-dependent expansion coefficients. The authors give explicit formulae of the method for the case of two colliding atoms (or ions).

It is first found that the intrinsic parity of an operator under time reversal and the interpretation of the operator as coordinate- or momentum-like in a TDHF calculation are not simply related. This is because the TDHF particle-hole basis is, in general, complex. The TDHF equation is then reformulated in the plane tangent to the Slater determinant manifold. This plane is spanned by the particle-hole basis. The particle-hole matrix elements of the Hartree-Fock Hamiltonian define the energy gradient vector in this tangent plane. This gradient is real when the Slater determinant is real. A TDHF calculation initiated from a realmore » determinant induces, during the first infinitesimal time step, a purely imaginary variation of this determinant along the gradient. The gradient is thus identified with the matrix elements of a boost operator. The next infinitesimal time step defines, in turn, a displacement operator. These operators are retained as collective if the TDHF path is stable under changes of velocities. Various criteria are found for this stability condition. The theory cannot be applied straightforwardly to translations and rotations for there is no energy gradient to generate coordinate operators. Particle-hole matrix elements of boost operators can be obtained, however, by a multiplication by i of the matrix elements of displacement operators, since the latter are known explicitly. It is finally found that the rotation of a wavefunction is contradictory with angular momentum conservation in general. Conservation can be ensured by a rotation of the density only and a more elaborate evolution of the velocity field.« less

The mean-field description of low-energy heavy-ion scattering is extended to include the residual nucleon--nucleon interaction. The collision term is derived from a random-matrix model for this interaction in a weak-coupling limit. Particular attention is paid to justifying the approximations made in terms of the times scales typical of nuclei, and to the conservation of energy and particle number.