Solution of the Skyrme-Hartree–Fock–Bogolyubovequations in the Cartesian deformed harmonic-oscillator basis. (VIII) hfodd (v2.73y): A new version of the program

Abstract

We describe the new version (v2.73y) 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, we have implemented the following new features: (i) full proton–neutron mixing in the particle–hole channel for Skyrme functionals, (ii) the Gogny force in both particle–hole and particle–particle channels, (iii) linear multi-constraint method at finite temperature, (iv) fission toolkit including the constraint on the number of particles in the neck between two fragments, calculation of the interaction energy between fragments, and calculation of the nuclear and Coulomb energy of each fragment, (v) the new version 200d of the code hfbtho, together with an enhanced interface between hfbtho and hfodd, (vi) parallel capabilities, significantly extended by adding several restart options for large-scale jobs, (vii) the Lipkin translational energy correction method with pairing, (viii) higher-order Lipkin particle-number corrections, (ix) interface to a program plotting single-particle energies or Routhians, (x) strong-force isospin-symmetry-breaking terms, and (xi) the Augmented Lagrangian Method for calculations with 3D constraints on angular momentum and isospin. Finally, an important bug related to the calculation of the entropy at finite temperature and several other little significant errors of the previous published version were corrected. Program summaryTitle of the program:hfodd (v2.73y)Program Files doi:http://dx.doi.org/10.17632/3b28fs62wc.1Licensing provisions: GPL v3Programming language: FORTRAN-90Journal reference of previous version: N. Schunck, J. Dobaczewski, J. McDonnell, W. Satuła, J. Sheikh, A. Staszczak, M. Stoitsov, and P. Toivanen, Comput. Phys. Comm. 183 (2012) 166-192.Does the new version supersede the previous one: YesNature 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. For the density functional generated by a zero-range velocity-dependent Skyrme interaction, the nuclear mean field is quasilocal. This 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. Similarly, the local particle–particle density functional, generated by a zero-range interaction, allows for a simple implementation of pairing effects within the Hartree–Fock–Bogolyubov method. For finite-range interactions, like Coulomb, Yukawa, or Gogny interaction, the nuclear mean field becomes nonlocal, but using the spatial separability of the deformed harmonic-oscillator basis in three Cartesian directions, the self-consistent calculations can be efficiently performed.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 or Gogny effective interactions and zero-range or finite-range pairing interactions. The expansion coefficients are determined by the iterative diagonalization of the mean-field Hamiltonians or Routhians which depend non-linearly on the local or nonlocal neutron, proton, or mixed proton–neutron 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. Comm. 102 (1997) 166.Summary of revisions:1.Full proton–neutron mixing in the particle–hole channel for Skyrme functionals was implemented.2.The Gogny force was implemented in both particle–hole and particle–particle channels.3.Linear multi-constraint method based on the cranking approximation of the QRPA matrix was extended at finite temperature.4.Fission toolkit includes the constraint on the number of particles in the neck between two fragments, calculation of the interaction energy between fragments, and calculation of the nuclear and Coulomb energy of each fragment.5.The HFBTHO module was updated to version 200d, and an enhanced interface between HFBTHO and HFODD was implemented.6.Parallel capabilities were significantly extended by adding several restart options for large-scale jobs.7.The Lipkin translational energy correction method with pairing was implemented.8.Higher-order Lipkin particle-number corrections were implemented.9.Interface to a program plotting single-particle energies or Routhians was added.10.Strong-force isospin-symmetry-breaking terms were implemented.11.The Augmented Lagrangian Method for calculations with 3D constraints on angular momentum and isospin was implemented.12.An important bug related to the calculation of the entropy at finite temperature and several other little significant errors of the previous published version were corrected.Unusual features of the program: The user must have access to (i) the LAPACK subroutines zhpev, zhpevx, zheevr, or zheevd, which diagonalize complex hermitian matrices, (ii) the LAPACK subroutines dgetri and dgetrf which invert arbitrary real matrices, (iii) the LAPACK subroutines dsyevd, dsytrf and dsytri which compute eigenvalues and eigenfunctions of real symmetric matrices and (iv) the LINPACK subroutines zgedi and zgeco, which invert arbitrary complex matrices and calculate determinants, (v) the BLAS routines dcopy, dscal, dgeem and dgemv for double-precision linear algebra and zcopy, zdscal, zgeem and zgemv for complex 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/.