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Manuscript Title: B-spline finite elements and their efficiency in solving relativistic mean field equations.
Authors: W. Poschl
Program title: bspFEM.cc
Catalogue identifier: ADHP_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 112(1998)42
Programming language: C++.
Operating system: Unix.
Keywords: Nuclear physics, Theoretical methods, B-splines, Finite element method, Lagrange type shape, Functions, Relativistic mean-field, Theory, Mean-field approximation, Spherical nuclei, Dirac equations, Klein-gordon equations, Classes.
Classification: 17.16.

Nature of problem:
The ground-state of a spherical nucleus is described in the framework of relativistic mean field theory in coordinate space. The model describes a nucleus as a relativistic system of baryons and mesons. 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 equations), and differential equations for the meson and photon fields (Klein-Gordon equations). Two methods are compared which allow 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. Finite elements of arbitrary order are used on uniform radial mesh. B-splines are used as shape functions in the finite elements. 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.