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We describe the new version 3.00 of the code hfbtho that solves the nuclear Hartree–Fock (HF) or Hartree–Fock–Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the full Gogny force in both particle–hole and particle–particle channels, (ii) the calculation of the nuclear collective inertia at the perturbative cranking approximation, (iii) the calculation of fission fragment charge, mass and deformations based on the determination of the neck, (iv) the regularization of zero-range pairing forces, (v) the calculation of localization functions, (vi) a MPI interface for large-scale mass table calculations. PROGRAM SUMMARY Program title: hfbtho v3.00 Program Files doi: http://dx.doi.org/10.17632/c5g2f92by3.1 Licensing provisions: GPL v3 Programming language: FORTRAN-95 Journal reference of previous version: M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Comput. Phys. Commun. 184 (2013). Does the new version supersede the previous one: Yes Summary of revisions: 1. the Gogny force in both particle–hole and particle–particle channels was implemented; 2. the nuclear collective inertia at the perturbative cranking approximation was implemented; 3. fission fragment charge, mass and deformations were implemented based on the determination of the position of the neck between nascent fragments; 4. the regularization method of zero-range pairing forces was implemented; 5. the localization functions of the HFB solution were implemented; 6. a MPI interface for large-scale mass table calculations was implemented. Nature of problem: hfbtho is a physics computer code that is used to model the structure of the nucleus. It is an implementation of the energy density functional (EDF) approach to atomic nuclei, where the energy of the nucleus is obtained by integration over space of some phenomenological energy density, which is itself a functional of the neutron and proton intrinsic densities. In the present version of hfbtho , the energy density derives either from the zero-range Skyrme or the finite-range Gogny effective two-body interaction between nucleons. Nuclear super-fluidity is treated at the Hartree–Fock–Bogolyubov (HFB) approximation. Constraints on the nuclear shape allows probing the potential energy surface of the nucleus as needed e.g., for the description of shape isomers or fission. The implementation of a local scale transformation of the single-particle basis in which the HFB solutions are expanded provide a tool to properly compute the structure of weakly-bound nuclei. 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 or the finite-range Gogny force until a self-consistent solution is found. A previous version of the program was presented in M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Comput. Phys. Commun. 184 (2013) 1592–1604 with much of the formalism presented in the original paper M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, P. Ring, Comput. Phys. Commun. 167 (2005) 43–63. Additional comments: The user must have access to (i) the LAPACK subroutines dsyeevr , 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/ . [ABSTRACT FROM AUTHOR]

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 summary Title of the program: hfodd (v2.73y) Program Files doi: http://dx.doi.org/10.17632/3b28fs62wc.1 Licensing provisions: GPL v3 Programming language: FORTRAN-90 Journal 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: 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. 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/ . [ABSTRACT FROM AUTHOR]

Abstract: We derive a formalism, the separation method, for the efficient and accurate calculation of two-body matrix elements for a Gaussian potential in the cylindrical harmonic-oscillator basis. This formalism is of critical importance for Hartree–Fock and Hartree–Fock–Bogoliubov calculations in deformed nuclei using realistic, finite-range effective interactions between nucleons. The results given here are also relevant for microscopic many-body calculations in atomic and molecular physics, as the formalism can be applied to other types of interactions beyond the Gaussian form. The derivation is presented in great detail to emphasize the methodology, which relies on generating functions. The resulting analytical expressions for the Gaussian matrix elements are checked for speed and accuracy as a function of the number of oscillator shells and against direct numerical integration. [Copyright &y& Elsevier]