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Manuscript Title: Solution of the Skyrme-Hartree-Fock equations in the Cartesian deformed harmonic-oscillator basis. (III) HFODD (v1.75r): a new version of the program.
Authors: J. Dobaczewski, J. Dudek
Program title: HFODD (v1.75r)
Catalogue identifier: ADFL_v1_1
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 131(2000)164
Programming language: Fortran.
Computer: CRAY C-90, SG Power Challenge L, IBM RS/6000, Pentium-II, Athlon.
Operating system: UNIX, UNICOS, IRIX, AIX, LINUX.
RAM: 10M words
Word size: 64
Keywords: Nuclear physics, 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.
Classification: 17.22.

Nature of 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.

Solution method:
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, 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 Q22 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.

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).

Unusual features:
The user must have 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/comple x16/zhpev.f The code is written in single-precision for 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.

Running time:
One Hartree-Fock iteration for the superdeformed, rotating, parity conserving state of 152 66Dy86 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 J(2) can be obtained within one hour of CPU on the CRAY C-90, or within three hours of CPU on the Athlon-550 MHz 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 neighbouring rotational frequency.