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Manuscript Title: Coordinate-space solution of the Skyrme-Hartree-Fock-Bogolyubov equations within spherical symmetry. The program HFBRAD (v1.00)
Authors: K. Bennaceur, J. Dobaczewski
Program title: HFBRAD (v1.00)
Catalogue identifier: ADVM_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 168(2005)96
Programming language: Fortran-95.
Computer: Pentium-III, Pentium-IV.
Operating system: LINUX, Windows.
RAM: 30 MBytes
Word size: The code is written with a type real corresponding to 32-bit on any machine. This is achieved using the intrinsic function selected_real_kind at the beginning of the code and asking for at least 12 significant digits. This can be easily modified by asking for more significant digits if the architecture of the computer can handle it.
Keywords: Hartree-Fock, Hartree-Fock-Bogolyubov, Skyrme interaction, Self-consistent mean-field, Nuclear many-body problem, Pairing, Nuclear radii, Single-particle spectra, Coulomb field.
PACS: 07.05.T, 21.60.-n, 21.60.Jz.
Classification: 17.22.

Nature of problem:
For a self-consistent description of nuclear pair correlations, both the particle-hole (field) and particle-particle (pairing) channels of the nuclear mean field must be treated within the common approach, which is the Hartree-Fock-Bogolyubov theory. By expressing these fields in spatial coordinates one can obtain the best possible solutions of the problem; however, without assuming specific symmetries the numerical task is often too difficult. This is not the case when the spherical symmetry is assumed, because then the, one-dimensional differential equations can be solved very efficiently. Although the spherically symmetric solutions are physically meaningful only for magic and semi-magic nuclei, the possibility of obtaining them within tens of seconds of the CPU makes them a valuable element of studying nuclei across the nuclear chart, including those near or at the drip lines.

Solution method:
The program determines the two-component Hartree-Fock-Bogolyubov quasiparticle wave functions on the lattice of equidistant points in the radial coordinate. This is done by solving the eigensystem of two second-order differential equations by using the Numerov method. A standard iterative procedure is then used to find self-consistent solutions for the nuclear product wave functions and densities.

The main restriction is related to the assumed spherical symmetry.

Running time:
One Hartree-Fock iteration takes about 0.4 sec for a medium mass nucleus, convergence is achieved in about 40 sec.