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Manuscript Title: Computer program for the time-evolution of a nuclear system in relativistic mean-field theory.
Authors: H. Berghammer, D. Vretenar, P. Ring
Program title: TDRMFT.C
Catalogue identifier: ADBI_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 88(1995)293
Programming language: C.
Computer: CRAY-YMP.
Operating system: UNIX.
Keywords: Nuclear physics, Theoretical methods, Time-dependent, Relativistic mean, Field theory, Collective motion in, Nuclei, Giant resonances, Coulomb dissociaton.
Classification: 17.16.

Nature of problem:
Relativistic quantum field models have been successfully applied to nuclear matter and finite nucleus calculations. In comparison with conventional non-relativistic descriptions, relativistic models explicitly include mesonic degrees of freedom, and treat the nucleons as Dirac particles. We use a time dependent version of the relativistic mean field model to investigate the dynamics of small and large amplitude collective motion in nuclei. For a given set of initial conditions (stationary solution for the ground-state, initial velocities of the proton and neutron densities, initial deformations), the model describes the time evolution of the nuclear system.

Solution method:
The time-evolution of a nucleus is described by a coupled system of partial differential equations for the nucleons (Dirac equation), and for mesons and photons (Klein-Gordon equations). In the present version of the program, axial symmetry is assumed and the coupled system of equations of motion is integrated numerically on a finite mesh in the (r,z) plane (cylindrical coordinates) of the center-of-mass system of the nucleus. The set of eight coupled first order partial differential equations for the amplitudes of the Dirac spinors is integrated using the staggered leapfrog difference scheme. At each step in time, the potentials that enter the Dirac equation are obtained as solution of elliptic time-independent Klein-Gordon equations. The equations are solved using a simultaneous over-relaxation (SOR) algorithm.

The coupled system of equations of motion is integrated under the assumption of axial symmetry. Initial conditions are chosen in such a way that there is no contribution from the pion field and the phi- components of the vector fields. It is only necessary to integrate the equations of motion for half of the nucleons. There is also another version of the program available, which does not impose these restrictions on initial conditions. Calculations are simplified by neglecting the time derivatives in the Klein-Gordon equations for the meson fields. This means that retardation efects for the meson fields are neglected. The present version of the program has been applied to doubly closed-shell nuclei. It necessitates starting with a spherically symmetric ground state. The extension to a nucleus with an axially deformed ground state is straightforward. The code is not only very much time consuming, but will use ~ 10-20 Mbytes of memory for a medium heavy nucleus.

Running time:
days to weeks on a networked work-station.