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Manuscript Title: Application of the finite element method in self-consistent relativistic mean field calculations.
Authors: W. Poschl, D. Vretenar, P. Ring
Program title: slabFEM.cc
Catalogue identifier: ADED_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 99(1996)128
Programming language: C++.
Computer: Unix work-station.
Operating system: Unix.
Keywords: Nuclear physics, Theoretical methods, Relativistic mean field Theory, Nuclear matter, Dirac equation, Finite element method, Bisection method, Classes.
Classification: 17.16.

Nature of problem:
Relativistic quantum field model calculations provide a detailed description of nuclear matter and properties of finite nuclei. In comparison with conventional nonrelativistic descriptions, relativistic models explicitly include mesonic degrees of freedom and consider the nucleons as Dirac particles. Nucleons interact in a relativistic covariant manner through the exchange of virtual mesons. A simplified version of the relativistic mean-field model is used to describe the ground state of a one-dimensional slab of nuclear matter.

Solution method:
A slab of nuclear matter is described by a coupled system of partial differential equations for the nucleons (Dirac equation), and for the meson fields (Klein-Gordon equations). A method is presented which allows a simple, self-consistent solution based on finite element analysis. Using a formulation based on weighted residuals, the coupled system of Dirac and Klein-Gordon equations is transformed into a generalized algebraic eigenvalue problem and a system of nonlinear algebraic equations, respectively. A simple linear finite element ansatz is used on a uniform one-dimensional mesh. The generalized eigenvalue problem is solved in narrow windows of the eigenparameter using a highly efficient bisection method for band matrices.

Restrictions:
In the present version of the code we only consider a one-dimensional slab of nuclear matter extending homogeneously to infinity in the perpendicular plane.