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[Licence| Download | New Version Template] adhp_v1_0.tar.gz(22 Kbytes)
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.

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