J.Dobaczewski^{a,b,}^{1}
and J. Dudek^{a,}^{2}

^{a}*Institute de Recherches Subatomiques,
CNRS-IN*_{2}*P*_{3}*/Université Louis Pasteur,
F-67037 Strasbourg Cedex 2, France
*

ul. Hoza 69, PL-00681 Warsaw, Poland

**Abstract**

We describe the new version (v1.75r) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock problem by using the Cartesian deformed harmonic-oscillator basis. Three minor errors that went undetected in the previous version have been corrected. The new version contains an interface to the LAPACK subroutine ZHPEV. Several methods of terminating the Hartree-Fock iteration procedure, and an algorithm that allows to follow the diabatic configurations, have been implemented.

PACS numbers: 07.05.T, 21.60.-n, 21.60.Jz

**NEW VERSION PROGRAM SUMMARY**

*Title of the program:* HFODD
(v1.75r)

*Catalogue number:*

*Program obtainable from:*
CPC Program Library, Queen's University of Belfast, N. Ireland
(see application form in this issue)

*Reference in CPC for earlier version of program:*
J. Dobaczewski and J. Dudek, Comput. Phys. Commun. **102** (1997) 183 (v1.60r).

*Catalogue number of previous version:*
ADFL

*Licensing provisions:* none

*Does the new version supersede the previous one:* yes

*Computers on which the program has been tested:*
CRAY C-90, SG Power Challenge L, IBM RS/6000,
Pentium-II, Athlon

*Operating systems:* UNIX, UNICOS, IRIX, AIX, LINUX

*Programming language used:* FORTRAN-77

*Memory required to execute with typical data:* 10 Mwords

*No. of bits in a word:*
The code is written in
single-precision for the use on a 64-bit processor. The compiler
option `-r8` or `+autodblpad` (or equivalent) has to be used
to promote all real and complex single-precision floating-point items
to double precision when the code is used on a 32-bit machine.

*Has the code been vectorised?:* Yes

*No. of lines in distributed program:*
23 987 (of which 10 445 are comments and separators)

*Keywords:*
Hartree-Fock; Skyrme interaction;
Self-consistent mean-field;
Nuclear many-body problem; Superdeformation;
Quadrupole deformation; Octupole deformation; Pairing;
Nuclear radii; Single-particle spectra;
Nuclear rotation; High-spin states;
Moments of inertia; Level crossings; Harmonic oscillator;
Coulomb field; Point symmetries

*Nature of physical problem*

The nuclear mean-field and an analysis of its symmetries in realistic cases
are the main
ingredients of a description of nuclear states. Within the
Local Density Approximation, or for a zero-range velocity-dependent
Skyrme interaction, the nuclear mean-field is local and velocity
dependent. The locality allows for an effective and fast solution of the
self-consistent Hartree-Fock
equations, even for heavy nuclei, and for various nucleonic
(*n*-particle *n*-hole)
configurations, deformations, excitation energies, or angular momenta.

*Method of solution*

The program uses the Cartesian harmonic oscillator basis to
expand single-particle wave functions of neutrons and protons
interacting by means of the Skyrme effective interaction. The expansion
coefficients are determined by the iterative diagonalization of
the mean field Hamiltonians or Routhians which depend nonlinearly
on the local neutron and proton densities. Suitable constraints
are used to obtain states corresponding to a given configuration,
deformation or angular momentum. The method of solution has been
presented in: J. Dobaczewski and J. Dudek, Comput. Phys. Commun. **102** (1997) 166.

*Summary of revisions*

- 1.
- An error in the calculation of one of the time-odd mean-field potentials has been corrected.
- 2.
- A factor in the calculation of the multipole moment
*Q*_{22}has been corrected. - 3.
- Scaling of the coupling constants has been corrected.
- 4.
- An interface to the LAPACK subroutine ZHPEV has been created.
- 5.
- Several methods of terminating the Hartree-Fock iteration procedure have been implemented.
- 6.
- An algorithm that allows to follow the diabatic configurations has been implemented.
- 7.
- Saving of auxiliary data for a faster calculation of the Coulomb potential has been implemented.
- 8.
- Calculation of average quadrupole moments and radii of single-particle states has been added.
- 9.
- Calculation of the Bohr deformation parameters has been added.

*Restrictions on the complexity of the problem*

The main restriction is the CPU time required for calculations of heavy deformed nuclei and for a given precision required. One symmetry plane is assumed. Pairing correlations are only included in the BCS limit and for the conserved time-reversal symmetry (i.e., for non-rotating states in even-even nuclei).

*Typical running time*

One Hartree-Fock iteration for the superdeformed, rotating,
parity conserving state of
^{152}_{ 66}Dy_{86} takes about
nine seconds on the CRAY C-90 computer. Starting from the
Woods-Saxon wave functions, about fifty iterations are required
to obtain the energy converged within the precision of about
0.1keV. In case when every value of the angular velocity is
converged separately, the complete superdeformed band with
precisely determined dynamical moments
can be obtained
within one hour of CPU on the CRAY C-90, or within three
hours of CPU on the Athlon-550MHz processor. This time can be often
reduced by a factor of three when a self-consistent solution for a
given rotational frequency is used as a starting point for a
neighboring rotational frequency.

*Unusual features of the program*

The user must have an access to the NAGLIB subroutine F02AXE or to the ESSL or LAPACK subroutine ZHPEV which diagonalize complex hermitian matrices, or provide another subroutine which can perform such a task. The LAPACK subroutine ZHPEV can be obtained from the Netlib Repository at University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/cgi-bin/netlibfiles.pl?filename=/lapack/complex16/zhpev.f

**LONG WRITE-UP**

- Introduction
- Modifications introduced in version (v1.75r)
- Calculation of the density
- Calculation of the multipole moment
*Q*_{22} - Scaling of the coupling constants
- Diagonalization subroutines
- Terminating the Hartree-Fock iteration procedure
- Diabatic blocking
- Saving the Coulomb data
- Calculation of moments and radii
- Calculation of the Bohr deformation parameters

- Input data file
- Output file
- FORTRAN source file
- Acknowledgments
- Bibliography
- TEST RUN INPUT
- TEST RUN OUTPUT
- About this document ...