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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.

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