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Manuscript Title: Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (V) (v2.08k), a new version of the program
Authors: J. Dobaczewski, P. Olbratowski
Program title: HFODD; version. 2.08k
Catalogue identifier: ADFL_v2_1
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 167(2005)214
Programming language: Fortran.
Computer: SG Power Challenge L, Pentium-II, Pentium-III, AMD-Athlon.
Operating system: UNIX, LINUX, Windows-2000.
RAM: 10M words
Word size: 64
Keywords: Nuclear Physics, Hartree-Fock, Hartree-Fock-Bogolyubov, 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.
PACS: 07.05.T, 21.60.-n, 21.60.Jz.
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. Similar Local Density Approximation in the particle-particle channel, which is equivalent to using a zero-range interaction, allows for a simple implementation of pairing effects within the Hartree-Fock-Bogolyubov method.

Solution method:
The program uses the Cartesian harmonic oscillator basis to expand single-particle or single-quasiparticle wave functions of neutrons and protons interacting by means of the Skyrme effective interaction and zero-range pairing interaction. The expansion coefficients are determined by the iterative diagonalization of the mean field Hamiltonians or Routhians which depend non-linearly 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. Incorrect value of the "t0" force parameter for SLY5 has been corrected.
  2. Opening of an empty file "FILREC" for IWRIRE=-1 has been removed.
  3. Call to subroutine "OLSTOR" has been moved before that to "SPZERO". In this way, correct data transferred to "FLISIG", "FLISIM", "FLISIQ" or "FLISIZ" allow for a correct determination of the candidate states for diabatic blocking.
These corrections pertain to the user interface of the code and do not affect results performed for forces other than SLY5.

The main restriction is the CPU time required for calculations of heavy deformed nuclei and for a given precision required. Pairing correlations are only included for even-even nuclei and conserved simplex symmetry.

Unusual features:
The user must have access to the NAGLIB subroutine F02AXE or to the LAPACK subroutines ZHPEV or ZHPEVX, which diagonalize complex hermitian matrices, or provide another subroutine which can perform such a task. The LAPACK subroutines ZHPEV and ZHPEVX 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 and
http://netlib2.cs.utk.edu/cgi-bin/netlibfiles.pl?filename=/lapack/complex16/zhpev x.f respectively.
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.

Additional comments:
The actual output files obtained during user's test runs may differ from those provided in the distribution file. The differences may occur because various compilers may produce different results in the following aspects,

a. The initial Nilsson spectrum (the starting point of each run) is Kramers degenerate, and thus the diagonalization routine may return the degenrate states in arbitrary order and in arbitrary mixture. For an odd number of particles, one of these states becomes occupied, and the other one is left empty. Therefore, starting points of such runs can widely vary from compiler to compiler, and these differences cannot be controlled.

b. For axial shapes, two quadrupole moments (with respect to two different axes) become very small and their values reflect only a numerical noise. However, depending on which of these two moments is smaller, the intrinsic-frame Euler axes will differ, most often by 180 degrees. Hence, signs of some moments and angular momenta may vary from compiler to compiler, and these differences cannot be controlled.

These differences are insignificant. The final energies do not depend on them, although the intermediate results can.

Running time:
One Hartree-Fock iteration for the superdeformed, rotating, parity conserving state of 15266Dy86 takes about six seconds on the AMD-Athlon 1600+ processor. 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 the 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 forty minutes of CPU on the AMD-Athlon 1600+ 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.