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Manuscript Title: Relativistic Hartree-Bogoliubov theory in coordinate space: finite element solution for a nuclear system with spherical symmetry.
Authors: W. Poschl, D. Vretenar, P. Ring
Program title: spnRHBfem.cc
Catalogue identifier: ADFX_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 103(1997)217
Programming language: C++.
Operating system: Unix.
Keywords: Nuclear physics, Hartree-fock, Relativistic hartree Bogoliubov theory, Mean-field approximation, Spherical nuclei, Pairing, Dirac-hartree Bogoliubov equations, Klein-gordon equation, Finite element method, Bisection method, Classes.
Classification: 17.22.

Nature of problem:
The ground-state of a spherical nucleus is described in the framework of relativistic Hartree-Bogoliubov 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. Pairing correlations are described by finite range Gogny forces.

Solution method:
An atomic nucleus is described by a coupled system of partial integro- differential equations for the nucleons (Dirac-Hartree-Bogoliubov equations), and differential equations 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- Hartree-Bogoliubov 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 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.