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Manuscript Title: Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VI) HFODD (v2.40h): a new version of the program.
Authors: J. Dobaczewski, W. Satula, B.G. Carlsson, J. Engel, P. Olbratowski, P. Powalowski, M. Sadziak, J. Sarich, N. Schunck, A. Staszczak, M. Stoitsov, M. Zalewski, H. Zdunczuk
Program title: HFODD (v2.40h)
Catalogue identifier: ADFL_v2_2
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 180(2009)2361
Programming language: FORTRAN-77 and Fortran-90.
Computer: Pentium-III, AMD-Athlon, AMD-Opteron.
Operating system: UNIX, LINUX, Windows XP.
Has the code been vectorised or parallelized?: Yes, vectorised
RAM: 10 Mwords
Word size: 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.
Keywords: 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, Yukawa interaction, Angular-momentum projection, Generator Coordinate Method, Schiff moments.
PACS: 07.05.T, 21.60.-n, 21.60.Jz.
Classification: 17.22.

External routines: Lapack (http://www.netlib.org/lapack/), Blas (http://www.netlib.org), linpack (http://www.netlib/linpack/)

Does the new version supersede the previous version?: Yes

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 [1].

Summary of revisions:
  1. Projection on good angular momentum (for the Hartree-Fock states) has been implemented.
  2. Calculation of the GCM kernels has been implemented.
  3. Calculation of matrix elements of the Yukawa interaction has been implemented.
  4. The BCS solutions for state-dependent pairing gaps have been implemented.
  5. The HFB solutions for broken simplex symmetry have been implemented.
  6. Calculation of Bohr deformation parameters has been implemented.
  7. Constraints on the Schiff moments and scalar multipole moments have been implemented.
  8. The DT2h transformations and rotations of wave functions have been implemented.
  9. The quasiparticle blocking for the HFB solutions in odd and odd-odd nuclei has been implemented.
  10. The Broyden method to accelerate the convergence has been implemented.
  11. The Lipkin-Nogami method to treat pairing correlations has been implemented.
  12. The exact Coulomb exchange term has been implemented.
  13. Several utility options have been implemented.
  14. Three insignificant errors have been corrected.

The main restriction is the CPU time required for calculations of heavy deformed nuclei and for a given precision required.

Unusual features:
The user must have access to
  1. an implementation of the BLAS (Basic Linear Algebra Subroutines),
  2. the NAGLIB subroutine F02AXE, or LAPACK subroutines ZHPEV, ZHPEVX, or ZHEEVR, which diagonalize complex hermitian matrices, and
  3. the LINPACK subroutines ZGEDI and ZGECO, which invert arbitrary complex matrices and calculate determinants
or provide another set of subroutines that can perform such tasks.
The LAPACK and LINPACK subroutines and an unoptimized version of the BLAS can be obtained from the Netlib Repository at the University of Tennessee, Knoxville: http://www.netlib.org/.

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 0.1 keV. In the case where every value of the angular velocity is converged separately, the complete superdeformed band with precisely determined dynamical moments J(2) can be obtained in forty minutes of CPU time 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.

[1] J. Dobaczewski and J. Dudek, Comput. Phys. Commun. 102(1997) 166.