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Manuscript Title: Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis
(II) HFBTHO v2.00d: a new version of the program.
Authors: M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, S. Wild
Program title: HFBTHO v2.00d
Catalogue identifier: ADUI_v2_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 184(2013)1592
Programming language: FORTRAN-95.
Computer: Intel Pentium-III, Intel Xeon, AMD-Athlon, AMD-Opteron, Cray XT5, Cray XE6.
Operating system: UNIX, LINUX, WindowsXP.
RAM: 200 Mwords
Word size: 8 bits
Keywords: Hartree-Fock, Hartree-Fock-Bogolyubov, Nuclear many-body problem, Skyrme interaction, Self-consistent mean field, Density functional theory, Generalized energy density functional, Nuclear matter, Quadrupole deformation, Octupole deformation, Constrained calculations, Potential energy surface, Pairing, Particle number projection, Nuclear radii, Quasiparticle spectra, Harmonic oscillator, Coulomb field, Transformed harmonic oscillator, Finite temperature, Shared memory parallelism.
PACS: 07.05.T, 21.60.-n, 21.60.Jz.
Classification: 17.22.

Does the new version supersede the previous version?: Yes

Nature of problem:
The solution of self-consistent mean-field equations for weakly-bound paired nuclei requires a correct description of the asymptotic properties of nuclear quasiparticle wave functions. In the present implementation, this is achieved by using the single-particle wave functions of the transformed harmonic oscillator, which allows for an accurate description of deformation effects and pairing correlations in nuclei arbitrarily close to the particle drip lines.

Solution method:
The program uses the axial Transformed Harmonic Oscillator (THO) single-particle basis to expand quasiparticle wave functions. It iteratively diagonalizes the Hartree-Fock-Bogolyubov Hamiltonian based on generalized Skyrme-like energy densities and zero-range pairing interactions until a self-consistent solution is found. A previous version of the program was presented in: M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, P. Ring, Comput. Phys. Commun. 167 (2005) 43-63.

Reasons for new version:
Version 2.00d of HFBTHO provides a number of new options such as the optional breaking of reflection symmetry, the calculation of axial multipole moments, the finite temperature formalism for the HFB method, optimized multi-constraint calculations, the treatment of odd-even and odd-odd nuclei in the blocking approximation, and the framework for generalized energy density with arbitrary density-dependences. It is also the first version of HFBTHO to contain threading capabilities.

Summary of revisions:
  1. The modified Broyden method has been implemented,
  2. Optional breaking of reflection symmetry has been implemented,
  3. The calculation of all axial multipole moments up to λ = 8 has been implemented,
  4. The finite temperature formalism for the HFB method has been implemented,
  5. The linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations has been implemented,
  6. The blocking of quasi-particles in the Equal Filling Approximation (EFA) has been implemented,
  7. The framework for generalized energy density functionals with arbitrary density-dependence has been implemented,
  8. Shared memory parallelism via OpenMP pragmas has been implemented.

Restrictions:
Axial- and time-reversal symmetries are assumed.

Unusual features:
The user must have access to
(i) the LAPACK subroutines DSYEVD, DSYTRF and DSYTRI, and their dependencies, which compute eigenvalues and eigenfunctions of real symmetric matrices,
(ii) the LAPACK subroutines DGETRI and DGETRF, which invert arbitrary real matrices, and
(iii) the BLAS routines DCOPY, DSCAL, DGEMM and DGEMV for double-precision linear algebra
(or provide another set of subroutines that can perform such tasks). The BLAS and LAPACK subroutines can be obtained from the Netlib Repository at the University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/.

Running time:
Highly variable, as it depends on the nucleus, size of the basis, requested accuracy, requested configuration, compiler and libraries, and hardware architecture. An order of magnitude would be a few seconds for ground-state configurations in small bases Nmax ≈ 8 - 12, to a few minutes in very deformed configuration of a heavy nucleus with a large basis Nmax > 20.