K. Bennaceur

IPN Lyon, CNRS-IN2P3/UCB Lyon 1, Bât. Paul Dirac,

43, Bd. du 11 novembre 1918, 69622 Villeurbanne Cedex, France

bennaceur@ipnl.in2p3.fr

J. Dobaczewski

Institute of Theoretical Physics, Warsaw University

ul. Hoza 69, PL-00681 Warsaw, Poland

Department of Physics and Astronomy, The University of Tennessee,

Knoxville, Tennessee 37996, USA

Physics Division, Oak Ridge National Laboratory,

P.O. Box 2008, Oak Ridge, Tennessee 37831, USA

jacek.dobaczewski@fuw.edu.pl

IPN Lyon, CNRS-IN2P3/UCB Lyon 1, Bât. Paul Dirac,

43, Bd. du 11 novembre 1918, 69622 Villeurbanne Cedex, France

bennaceur@ipnl.in2p3.fr

J. Dobaczewski

Institute of Theoretical Physics, Warsaw University

ul. Hoza 69, PL-00681 Warsaw, Poland

Department of Physics and Astronomy, The University of Tennessee,

Knoxville, Tennessee 37996, USA

Physics Division, Oak Ridge National Laboratory,

P.O. Box 2008, Oak Ridge, Tennessee 37831, USA

jacek.dobaczewski@fuw.edu.pl

We describe the first version (v1.00) of the code HFBRAD which solves the Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov equations in the coordinate representation within the spherical symmetry. A realistic representation of the quasiparticle wave functions on the space lattice allows for performing calculations up to the particle drip lines. Zero-range density-dependent interactions are used in the pairing channel. The pairing energy is calculated by either using a cut-off energy in the quasiparticle spectrum or the regularization scheme proposed by A. Bulgac and Y. Yu.

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

**PROGRAM SUMMARY**

*Title of the program:* HFBRAD
(v1.00)

*Program obtainable from:*
CPC Program Library,
Queen's University of Belfast, N. Ireland

*Licensing provisions:* none

*Computers on which the program has been tested:*
Pentium-III, Pentium-IV

*Operating systems:* LINUX, Windows

*Programming language used:* FORTRAN-95

*Memory required to execute with typical data:*
30 MBytes

*No. of bits in a word:*
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.

*No. of processors used:* 1

*Has the code been vectorised?:* No.

*No. of bytes in distributed program, including test data, etc.:*
400 kbytes

*No. of lines in distributed program:* 5164
(of which 1635 are comments and separators)

*Nature of physical 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.

*Method of solution:*
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.
Standard iterative procedure is then used to find self-consistent
solutions for the nuclear product wave functions and densities.

*Restrictions on the complexity of the problem:*
The main restriction is related to the assumed spherical symmetry.

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

*Unusual features of the program:* none

**LONG WRITE-UP**

- Introduction
- The Skyrme Hartree-Fock-Bogolyubov equations
- Local densities
- Spherical symmetry
- The Hartree-Fock-Bogolyubov energy
- The Hartree-Fock-Bogolyubov mean fields
- The Hartree-Fock-Bogolyubov equations
- Asymptotic properties of the HFB wave functions
- Pairing correlations and divergence of the energy

- The effective Skyrme force
- Observables and single particle properties
- Hartree-Fock equivalent energies, radii, and nodes of quasiparticle wave functions
- Canonical basis
- Observables and other characteristic quantities of the system

- Numerical treatment of the problem

- Input data file

- Output files
- Examples

- Conclusion
- Acknowledgments
- Bibliography
- About this document ...