We describe the program HFBTHO for axially deformed configurational Hartree–Fock–Bogolyubov calculations with Skyrme-forces and zero-range pairing interaction using Harmonic-Oscillator and/or ...Transformed Harmonic-Oscillator states. The particle-number symmetry is approximately restored using the Lipkin–Nogami prescription, followed by an exact particle number projection after the variation. The program can be used in a variety of applications, including systematic studies of wide ranges of nuclei, both spherical and axially deformed, extending all the way out to nucleon drip lines.
Title of the program: HFBTHO (v1.66p)
Catalogue number: ADUI
Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland
Program summary URL:
http://cpc.cs.qub.ac.uk/summaries/ADUI
Licensing provisions: none
Computers on which the program has been tested: Pentium-III, Pentium-IV, AMD-Athlon, IBM Power 3, IBM Power 4, Intel Xeon
Operating systems: LINUX, Windows
Programming language used: FORTRAN-95
Memory required to execute with typical data: 59 MB when using
N
sh
=
20
No. of bits in a word: 64
No. of processors used: 1
Has the code been vectorized?: No
No. of bytes in distributed program, including test data, etc.: 195 285
No. of lines in distributed program: 12 058
Distribution format: tar.gz
Nature of physical 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.
Method of solution: The program uses the axially Transformed Harmonic Oscillator (THO) single-particle basis to expand quasiparticle wave functions. It iteratively diagonalizes the Hartree–Fock–Bogolyubov Hamiltonian based on the Skyrme-forces and zero-range pairing interaction until a self-consistent solution is found.
Restrictions on the complexity of the problem: Axial-, time-reversal-, and space-inversion symmetries are assumed. Only quasiparticle vacua of even–even nuclei can be calculated.
Typical running time: 4 s per iteration on an Intel Xeon 2.8 GHz processor when using
N
sh
=
20
Unusual features of the program: none
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We describe the new version 2.00d of the code hfbtho that solves the nuclear Skyrme-Hartree–Fock (HF) or Skyrme-Hartree–Fock–Bogoliubov (HFB) problem by using the cylindrical transformed deformed ...harmonic oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (EFA), (vii) framework for generalized energy density with arbitrary density-dependences, and (viii) shared memory parallelism via OpenMP pragmas.
Program title: HFBTHO v2.00d
Catalog identifier: ADUI_v2_0
Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUI_v2_0.html
Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland
Licensing provisions: GNU General Public License version 3
No. of lines in distributed program, including test data, etc.: 167228
No. of bytes in distributed program, including test data, etc.: 2672156
Distribution format: tar.gz
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
Classification: 17.22.
Does the new version supercede the previous version?: Yes
Catalog identifier of previous version: ADUI_v1_0
Journal reference of previous version: Comput. Phys. Comm. 167 (2005) 43
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 quasi-particle 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 quasi-particle wave functions. It iteratively diagonalizes the Hartree–Fock–Bogoliubov 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 dependences, 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.
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The fast computation of the Gauss hypergeometric function
F
1
2
with all its parameters complex is a difficult task. Although the
F
1
2
function verifies numerous analytical properties involving ...power series expansions whose implementation is apparently immediate, their use is thwarted by instabilities induced by cancellations between very large terms. Furthermore, small areas of the complex plane, in the vicinity of
z
=
e
±
i
π
3
, are inaccessible using
F
1
2
power series linear transformations. In order to solve these problems, a generalization of R.C. Forrey's transformation theory has been developed. The latter has been successful in treating the
F
1
2
function with real parameters. As in real case transformation theory, the large canceling terms occurring in
F
1
2
analytical formulas are rigorously dealt with, but by way of a new method, directly applicable to the complex plane. Taylor series expansions are employed to enter complex areas outside the domain of validity of power series analytical formulas. The proposed algorithm, however, becomes unstable in general when
|
a
|
,
|
b
|
,
|
c
|
are moderate or large. As a physical application, the calculation of the wave functions of the analytical Pöschl–Teller–Ginocchio potential involving
F
1
2
evaluations is considered.
Program title: hyp_2F1, PTG_wf
Catalogue identifier: AEAE_v1_0
Program summary URL:
http://cpc.cs.qub.ac.uk/summaries/AEAE_v1_0.html
Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence,
http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 6839
No. of bytes in distributed program, including test data, etc.: 63 334
Distribution format: tar.gz
Programming language: C++, Fortran 90
Computer: Intel i686
Operating system: Linux, Windows
Word size: 64 bits
Classification: 4.7
Nature of problem: The Gauss hypergeometric function
F
1
2
, with all its parameters complex, is uniquely calculated in the frame of transformation theory with power series summations, thus providing a very fast algorithm. The evaluation of the wave functions of the analytical Pöschl–Teller–Ginocchio potential is treated as a physical application.
Solution method: The Gauss hypergeometric function
F
1
2
verifies linear transformation formulas allowing consideration of arguments of a small modulus which then can be handled by a power series. They, however, give rise to indeterminate or numerically unstable cases, when
b
−
a
and
c
−
a
−
b
are equal or close to integers. They are properly dealt with through analytical manipulations of the Lanczos expression providing the Gamma function. The remaining zones of the complex plane uncovered by transformation formulas are dealt with Taylor expansions of the
F
1
2
function around complex points where linear transformations can be employed. The Pöschl–Teller–Ginocchio potential wave functions are calculated directly with
F
1
2
evaluations.
Restrictions: The algorithm provides full numerical precision in almost all cases for
|
a
|
,
|
b
|
, and
|
c
|
of the order of one or smaller, but starts to be less precise or unstable when they increase, especially through
a,
b, and
c imaginary parts. While it is possible to run the code for moderate or large
|
a
|
,
|
b
|
, and
|
c
|
and obtain satisfactory results for some specified values, the code is very likely to be unstable in this regime.
Unusual features: Two different codes, one for the hypergeometric function and one for the Pöschl–Teller–Ginocchio potential wave functions, are provided in C++ and Fortran 90 versions.
Running time: 20,000
F
1
2
function evaluations take an average of one second.
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The program of systematic large-scale self-consistent nuclear mass calculations that is based on the nuclear density functional theory represents a rich scientific agenda that is closely aligned with ...the main research directions in modern nuclear structure and astrophysics, especially the radioactive nuclear beam physics. The quest for the microscopic understanding of the phenomenon of nuclear binding represents, in fact, a number of fundamental and crucial questions of the quantum many-body problem, including the proper treatment of correlations and dynamics in the presence of symmetry breaking. Recent advances and open problems in the field of nuclear mass calculations are presented and discussed.
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