Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.

(IV) HFODD (v2.07f): a new version of the program.

J. Dobaczewski$^{a,b,c,d,}$¹ and P. Olbratowski$^{a,b,}$²
$^a$ Institute of Theoretical Physics, Warsaw University ul. Hoza 69, PL-00681 Warsaw, Poland
$^b$Institut de Recherches Subatomiques, CNRS-IN$_2$P$_3$/Université Louis Pasteur,
F-67037 Strasbourg Cedex 2, France
$^c$Department of Physics and Astronomy, The University of Tennessee,
Knoxville, Tennessee 37996, USA
$^d$Physics Division, Oak Ridge National Laboratory,
P.O. Box 2008, Oak Ridge, Tennessee 37831, USA

Abstract:

We describe the new version (v2.07f) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, all symmetries can be broken, which allows for calculations with angular frequency and angular momentum tilted with respect to the mass distribution. The new version contains an interface to the LAPACK subroutine ZHPEVX.

NEW VERSION PROGRAM SUMMARY

Title of the program: HFODD (v2.07f)

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. 131 (2000) 164 (v1.75r).

Catalogue number of previous version: ADML

Licensing provisions: none

Does the new version supersede the previous one: yes

Computers on which the program has been tested: SG Power Challenge L, Pentium-II, Pentium-III, AMD-Athlon

Operating systems: UNIX, LINUX, Windows-2000

Programming language used: FORTRAN-77 and FORTRAN-90

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: 43 308 (of which 19 386 are comments and separators)

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; Pairing; 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. 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.

Method of solution

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. Two insignificant errors have been corrected.
2. Breaking of all the three plane-reflection symmetries has been implemented.
3. Breaking of all the three time-reversal$\times$plane-reflection symmetries has been implemented.
4. Conservation of parity with simultaneously broken simplex has been implemented.
5. Tilted-axis cranking has been implemented.
6. Cranking with isovector angular frequency has been implemented.
7. Quadratic constraint on tilted angular momentum has been added.
8. Constraint on the vector product of angular frequency and angular momentum has been added.
9. Calculation of surface multipole moments has been added.
10. Constraints on surface multipole moments have been added.
11. Calculation of magnetic moments has been added.
12. Calculation of multipole and surface multipole moments in the center-of-mass reference frame has been added.
13. Calculation of multipole, surface multipole, and magnetic moments in the principal-axes (intrinsic) reference frame has been added.
14. Calculation of angular momenta in the center-of-mass and principal-axes reference frames has been added.
15. New single-particle observables for a diabatic blocking have been added.
16. Solution of the Hartree-Fock-Bogolyubov equations has been implemented.
17. Non-standard spin-orbit energy density has been implemented.
18. Non-standard center-of-mass corrections have been implemented.
19. Definition of the time-odd terms through the Landau parameters has been implemented.
20. Definition of Skyrme forces taken from the literature now includes the force parameters as well as the value of the nucleon mass and the treatment of tensor, spin-orbit, and center-of-mass terms specific to the given force.
21. Interface to the LAPACK subroutine ZHPEVX has been implemented.
22. Computer memory management has been improved by implementing the memory-allocation features available within FORTRAN-90.

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. Pairing correlations are only included for even-even nuclei and conserved simplex symmetry.

Typical running time

One Hartree-Fock iteration for the superdeformed, rotating, parity conserving state of $^{152}_{~66}$Dy$_{86}$ 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 case when every value of the angular velocity is converged separately, the complete superdeformed band with precisely determined dynamical moments ${{\cal J}^{(2)}}$ can be obtained within 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.

Unusual features of the program

The user must have an 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/zhpevx.f
respectively.

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