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Manuscript Title: Application of finite element methods in relativistic mean-field theory: spherical nucleus.
Authors: W. Poschl, D. Vretenar, A. Rummel, P. Ring
Program title: sphnucFEM.cc
Catalogue identifier: ADFG_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 101(1997)75
Programming language: C++.
Computer: Unix work-station.
Operating system: Unix.
Keywords: Nuclear physics, Theoretical methods, Relativistic mean field, Theory, Nuclear matter, Spherical nuclei, Dirac equation, Klein-gordon equation, Finite element method, Bisection method, Classes.
Classification: 17.16.

Nature of problem:
The ground-state of a spherical nucleus is described in the framework of relativistic mean-field theory. The model explicitly includes mesonic degrees of freedom and describes the nucleons as Dirac particles. Nucleons interact in a relativistic covariant manner through the exchange of virtual mesons: the isoscalar scalar sigma-meson, the isoscalar vector omega-meson and the isovector vector rho-meson. The model is based on the one boson exchange description of the nucleon- nucleon interaction.

Solution method:
An atomic nucleus is described by a coupled system of partial differential equations for the nucleons (Dirac equation), and for the meson and photon 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 systems of linear and nonlinear algebraic equations, respectively. Four different types of finite elements (linear, quadratic, cubic and 4th order shape functions), are used on adaptive non-uniform radial mesh. The generalized eigenvalue problem is solved in narrow windows of the eigenparameter using a highly efficient bisection method for band matrices. A biconjugate gradient method is used for the solution of systems of linear and nonlinear algebraic equations.

Restrictions:
In the present version of the code we only consider nuclear systems with spherical symmetry.