We describe a new version of the Ev8 code that solves the nuclear Skyrme-Hartree-Fock+BCS problem using a 3-dimensional cartesian mesh. Several new features have been implemented with respect to the earlier version published in 2005. In particular, the numerical accuracy has been improved for a given mesh size by (i) implementing a new solver to determine the Coulomb potential for protons, and (ii) implementing a more precise method to calculate the derivatives on a mesh that had already been implemented earlier in our beyond-mean-field codes. The code has been made very flexible to enable the use of a large variety of Skyrme energy density functionals that have been introduced in the last years. Finally, the treatment of the constraints that can be introduced in the mean-field equations has been improved. The code Ev8 is today the tool of choice to study the variation of the energy of a nucleus from its ground state to very elongated or triaxial deformations with a well-controlled accuracy.Program summaryProgram title: Ev8Catalogue identifier: ADWA_v2_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADWA_v2_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 29956No. of bytes in distributed program, including test data, etc.: 235072Distribution format: tar.gz Programming language: FORTRAN-90.Computer: AMD Opteron 6274, AMD Opteron 6134, AMD Opteron 2378, Intel Core i7-4700HQ.Operating system: Unix, Linux, OS X.RAM: On the order of 64 megabytes for the examples provided.Classification: 17.22.Catalogue identifier of previous version: ADWA_v1_0Journal reference of previous version: Comput. Phys. Comm. 171(2005)49Does the new version supersedethe previous version?: Yes, but when used in the same conditions both codes give the same result.Nature of problem:By means of the Hartree-Fock+BCS method for Skyrme-type energy density functionals, Ev8 allows the study of the evolution of the binding energy of even-even atomic nuclei for various shapes determined by the most general quadrupole and monopole constraints.Solution method:The program expands the single-particle wave-functions on a 3D Cartesian mesh. The nonlinear meanfield equations are solved by the imaginary time step method. A quadratic constraint is used to obtain states corresponding to given values of the monopole and quadrupole operators.Reasons for new version:The code has been generalized in several directions. The main changes concern the energy density functional that is more general than previously (including now tensor terms) and the accuracy of the final result that has been significantly improved by a new algorithm to determine the Coulomb potential. Several other changes should make the code more user friendly than it was before.Summary of revisions:1. Skyrme energy functionals with tensor terms;2. Improved accuracy for calculating derivatives;3. Improved accuracy for solving Coulomb problem;4. Improvement of the numerics of constraints;Restrictions:Ev8 assumes time-reversal invariance and nuclear shapes exhibiting three plane-reflection symmetries. Pairing correlations are treated at the BCS level of approximation.Running time:A few minutes for the examples provided, which concern rather heavy nuclei in modest boxes with an initial guess of Nilsson wavefunctions. (C) 2014 Elsevier B.V. All rights reserved.

Pairing correlations in the even-even A = 102 - 130 Sn isotopes are discussed, based on the Richardson-Gaudin variables in an exact Woods-Saxon plus reduced BCS pairing framework. The integrability of the model sheds light on the pairing correlations, in particular on the previously reported sub-shell structure.

Superdeformed bands are rotational sequences of states associated with the collective motion of a nucleus trapped in a secondary potential well of large deformation. As such, superdeformed states do not interact with the states at normal deformation over a large range of spins. They provide a unique opportunity to test nuclear models mid interactions in a regime very different from that applying to normal states. In particular, in a few cases, information about pairing correlations can be readily extracted from the experimental data. These correlations also play an important role in the mechanism responsible for deexcitation of superdeformed bands to the normally deformed states.

It has recently been shown that the linear response theory in symmetric nuclear matter can be used as a tool for detecting finite-size instabilities for different Skyrme functionals. In particular, it has been shown that there is a correlation between the density at which instabilities occur in infinite matter and the instabilities in finite nuclei. In this paper, we present a new fitting protocol that uses this correlation to add a new additional constraint in symmetric infinite nuclear matter in order to ensure the stability of finite nuclei against matter fluctuation in all spin and isospin channels. As an application, we give the parameter set for a new Skyrme functional which includes central and spin–orbit parts and which is free from instabilities by construction.

We study the effect of the tensor terms in the Skyrme energy density functional in the superdeformed band of Dy-152 in the cranked HFB approach, focusing in particular on the so-called 'time-odd' terms.

The role of configuration mixing in the Pt region is investigated. The nature of the ground state changes smoothly, being spherical around mass A ∼ 174 and A ∼ 192 and deformed around the mid-shell N = 104 region. Interacting Boson Model with configuration mixing calculations are presented for deformations and isotope shifts. The assumption of the existence of two configurations with very different deformation provides a simple framework to explain the observed isotope shifts systematics.

The authors thank T. Duguet for the stimulating discussions that motivated the present article. We also acknowledge the fruitful discussions with K. Bennaceur, J. Dobaczewski, and M. Kortelainen. A.P. is also grateful to the University of Jyvaskyla and the FIDIPRO group for the warm hospitality during the time in which part of this work was realized. D.T. was supported in part by the ERANET-NuPNET grant SARFEN of the Polish National Centre for Research and Development (NCBiR) and by the Academy of Finland and the University of Jyvaskyla within the FIDIPRO program. J.N. was supported by Mineco (Spain), Grant No. FIS2014-51948-C2-1-P.

Generalized seniority provides a truncation scheme for the nuclear shell model, based on pairing correlations, which offers the possibility of dramatically reducing the dimensionality of the nuclear shell-model problem. Systematic comparisons against results obtained in the full shell-model space are required to assess the viability of this scheme. Here, we extend recent generalized seniority calculations for semimagic nuclei, the Ca isotopes, to open-shell nuclei, with both valence protons and valence neutrons. The even-mass Ti and Cr isotopes are treated in a full major shell and with realistic interactions, in the generalized seniority scheme with one broken proton pair and one broken neutron pair. Results for level energies, orbital occupations, and electromagnetic observables are compared with those obtained in the full shell-model space. We demonstrate that, even for the Ti isotopes, significant benefit would be obtained in going beyond the approximation of one broken pair of each type, while the Cr isotopes require further broken pairs to provide even qualitative accuracy.

This article extends previous studies on the effect of tensor terms in the Skyrme energy density functional by breaking of time-reversal invariance. We have systematically probed the impact of tensor terms on properties of superdeformed rotational bands calculated within the cranked Hartree-Fock-Bogoliubov approach for different parameterizations covering a wide range of values for the isoscalar and isovector tensor coupling constants. We analyze in detail the contribution of the tensor terms to the energies and dynamical moments of inertia and study their impact on quasi-particle spectra. Special attention is devoted to the time-odd tensor terms, the effect of variations of their coupling constants and finite-size instabilities.

Background: Symmetry restoration and configuration mixing in the spirit of the generator coordinate method based on energy density functionals have become widely used techniques in low-energy nuclear structure physics. Recently, it has been pointed out that these techniques are ill defined for standard Skyrme functionals, and a regularization procedure has been proposed to remove the resulting spuriosities from such calculations. This procedure imposes an integer power of the density for the density-dependent terms of the functional. At present, only dated parametrizations of the Skyrme interaction fulfill this condition.Purpose: To construct a set of parametrizations of the Skyrme energy density functional for multireference energy density functional calculations with regularization using the state-of-the-art fitting protocols.Method: The parametrizations were adjusted to reproduce ground-state properties of a selected set of doubly magic nuclei and properties of nuclear matter. Subsequently, these parameter sets were validated against properties of spherical and deformed nuclei.Results: Our parameter sets successfully reproduce the experimental binding energies and charge radii for a wide range of singly magic nuclei. Compared to the widely used SLy5 and to the SIII parametrization that has integer powers of the density, a significant improvement of the reproduction of the data is observed. Similarly, a good description of the deformation properties at A similar to 80 was obtained.Conclusions: We have constructed new Skyrme parametrizations with integer powers of the density and validated them against a broad set of experimental data for spherical and deformed nuclei. These parametrizations are tailor-made for regularized multireference energy density functional calculations and can be used to study correlations beyond the mean field in atomic nuclei.

The generalized seniority scheme has long been proposed as a means of dramatically reducing the dimensionality of nuclear shell model calculations, when strong pairing correlations are present. However, systematic benchmark calculations, comparing results obtained in a model space truncated according to generalized seniority with those obtained in the full shell model space, are required to assess the viability of this scheme. Here, we extend recent calculations for semimagic nuclei, the Ca isotopes, to include nuclei with both valence protons and valence neutrons, namely, the Ti and Cr isotopes, taken in a full major shell and with realistic interactions

The generalized seniority scheme has long been proposed as a means of dramatically reducing the dimensionality of nuclear shell-model calculations, when strong pairing correlations are present. However, systematic benchmark calculations, comparing results obtained in a model space truncated according to generalized seniority with those obtained in the full shell-model space, are required to assess the viability of this scheme. Here, a detailed comparison is carried out, for semimagic nuclei taken in a full major shell and with realistic interactions. The even-mass and odd-mass Ca isotopes are treated in the generalized seniority scheme, for generalized seniority v <= 3. Results for level energies, orbital occupations, and electromagnetic observables are compared with those obtained in the full shell-model space.

The case of Qˆ(χ1)⋅Qˆ(χ1)–Qˆ(χ2)⋅Qˆ(χ2) mixing in the interacting boson model is studied within its mean-field approximation. It is shown that the criticality conditions lead to two classes of solutions and that χ1 and χ2 need to have an opposite sign to allow for prolate–oblate shape coexistence. No evidence for a stable triaxial minimum is found. Phase diagrams for selected cases have been constructed.

We briefly discuss Hartree Fock Bogoliubov (HFB) plus self consistent cranking calculations for the superdeformed band in 194Hg, using the full Skyrme energy density functional including tensor terms in the p‐h channel.

The algebraic derivation of the matrix elements of the quadrupole collective variables within the canonical basis of SU(1, 1) x SO(5) is applied to a simple fermionic system with j = 1/2 to illustrate the method.