We analyse deformation mechanism in neutron-rich Cr, Fe and Ti isotopes with N=32-44 by means of a Skyrme-Hartree-Fock-Bogoliubov mean-field code employing a two-dimensional mesh representation in the cylindrical coordinate system. Evaluating systematically the quadrupole deformation energy, we show that the Skyrme parameter set SkM* gives a quadrupole instability around the neutron number N$\sim$38-42 in Cr isotopes, where the deformation energy curve suggests a transitional behavior with a shallow minimum extending to a large prolate deformation. Roles of a deformed N=38 gap and the position of the neutron g9/2 orbit are analysed in detail.
Proton and neutron densities from Skyrme-Hartree-Fock (SHF) calculations are used to generate non-local (g-folding) proton-nucleus optical potentials. They are formed by folding the densities with realistic nucleon-nucleon interactions. The potentials are then used to calculate differential cross sections and spin observables for proton scattering. Good agreement with data has been found, supporting those found previously when using SHF charge densities in analyses of electron scattering data. That agreement was improved by use of (shell model) occupation numbers to constrain the HF iterations…
We describe the program HFBTHO for axially deformed configurational Hartree-Fock-Bogoliubov 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.
We describe a new implementation of the quasiparticle random phase approximation (QRPA) in axially-symmetric deformed nuclei with Skyrme and volume-pairing energy-density functionals. After using a variety of tests to demonstrate the accuracy of the code in ^{24,26}Mg and ^{16}O, we report the first fully self-consistent application of the Skyrme QRPA to a heavy deformed nucleus, calculating strength distributions for several K^pi in ^{172}Yb. We present energy-weighted sums, properties of gamma-vibrational and low-energy K^pi=0^+ states, and the complete isovector E1 strength function. The QR…
We use the finite amplitude method (FAM), an efficient implementation of the quasiparticle random phase approximation, to compute beta-decay rates with Skyrme energy-density functionals for 3983 nuclei, essentially all the medium-mass and heavy isotopes on the neutron rich side of stability. We employ an extension of the FAM that treats odd-mass and odd-odd nuclear ground states in the equal filling approximation. Our rates are in reasonable agreement both with experimental data where available and with rates from other global calculations.
We use the finite amplitude method for computing charge-changing Skyrme-QRPA transition strengths in axially-deformed nuclei together with a modern Skyrme energy-density functional to fit several previously unconstrained parameters in the charge-changing time-odd part of the functional. With the modified functional we then calculate rates of beta-minus decay for all medium-mass and heavy even-even nuclei between the valley of stability and the neutron drip line. We fit the Skyrme parameters to a limited set of beta-decay rates, a set of Gamow-Teller resonance energies, and a set of spin-dipole…
We describe the new version 4.0 of the code hfbtho that solves the nuclear Hartree-Fock-Bogoliubov problem by using the deformed harmonic oscillator basis in cylindrical coordinates. In the new version, we have implemented the restoration of rotational, particle number, and reflection symmetry. The restoration of rotational symmetry does not require using bases closed under rotation. Furthermore, the SeaLL1 functional was added and the calculation of the Coulomb potential was improved. Finally, the code has been refactored to facilitate maintenance and future developments.
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 p…
We describe the new version 2.00d of the code HFBTHO that solves the nuclear Skyrme Hartree-Fock (HF) or Skyrme 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 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 mu…
The lowest quadrupole $γ$-vibrational $K^π=2^+$ states in axially deformed rare-earth (Nd, Sm, Gd, Dy, Er, Yb, Hf, W) and actinide (U) nuclei are systematically investigated within the separable random-phase-approximation (SRPA) based on the Skyrme functional. The energies $E_γ$ and reduced transition probabilities $B(E2)$ of $2^+_γ$-states are calculated with the Skyrme forces SV-bas and SkM$^*$. The energies of two-quasiparticle configurations forming the SRPA basis are corrected by using the pairing blocking effect. This results in a systematic downshift of $E_γ$ by 0.3-0.5 MeV and thus in …
Self-consistent axially symmetric Skyrme Hartree-Fock plus BCS calculations are performed to study the evolution of shapes with the number of nucleons in various chains of Yb, Hf, W, Os, and Pt isotopes from neutron number N=110 up to N=122. Potential energy curves are analyzed in a search for signatures of oblate-prolate phase shape transitions and results from various Skyrme and pairing forces are considered. Comparisons with results obtained with the Gogny interaction as well as with relativistic mean field calculations are presented. The role of the $γ$ degree of freedom is also discussed.
For axially symmetric even-even nuclei, we solve the Hartree-Fock-Bogoliubov (HFB) equations on a 2-D grid in cylindrical coordinates. The Skyrme SLy4 interaction is used for the mean field and a zero-range interaction for the pairing field. After decoupling the HFB lattice equations, we obtain quasiparticle states with equivalent single-particle energies up to 100 MeV or more. We present results for the Krypton isotope chain up to the two-neutron dripline, including two-neutron separation energies, pairing gaps, and quadrupole deformations for the ground states and isomeric minima.
With the use of the symmetry-unrestricted cranked Skyrme-Hartree-Fock method in the three-dimensional coordinate-mesh representation, we have carried out a systematic theoretical search for the superdeformed and hyperdeformed rotational bands in the mass A=30-50 region. Along the N=Z line, we have found superdeformed solutions in 32S, 36Ar, 40Ca, 44Ti, and hyperdeformed solutions in 36Ar, 40Ca, 44Ti, 48Cr. The superdeformed band in 40Ca is found to be extremely soft against both the axially symmteric (Y30) and asymmetric (Y31) octupole deformations. An interesting role of symmetry breaking in …
We present a systematic analysis of the description of odd nuclei by the Skyrme-Hartree-Fock approach augmented with pairing in BCS approximation and blocking of the odd nucleon. Current and spin densities in the Skyrme functional produce time-odd mean fields (TOMF) for odd nuclei. Their effect on basic properties (binding energies, odd-even staggering, separation energies and spectra) is investigated for the three Skyrme parameterizations SkI3, SLy6, and SV-bas. About 1300 spherical and axially-deformed odd nuclei with 16 < Z < 92 are considered. The calculations demonstrate that the TOMF eff…
We use the axially-deformed Skyrme Quasiparticle Random-Phase Approximation (QRPA) together with the SkM* energy-density functional, both as originally presented and with the time-odd part adjusted to reproduce the Gamow-Teller resonance energy in 208Pb, to calculate the matrix elements governing the neutrinoless double-beta decay of 76Ge, 130Te, 136Xe, and 150Nd. Our matrix elements in 130Te and 136Xe are significantly smaller than those of previous QRPA calculations, primarily because of the difference in pairing or deformation between the initial and final nuclei. In 76Ge and 150Nd our resu…
We report the first study of restoration of rotational symmetry and fluctuations of the quadrupole deformation in the framework of relativistic mean-field models. A model is developed which uses the generator coordinate method to perform configuration mixing calculations of angular momentum projected wave functions, calculated in a relativistic point-coupling model. The geometry is restricted to axially symmetric shapes, and the intrinsic wave functions are generated from the solutions of the constrained relativistic mean-field + BCS equations in an axially deformed oscillator basis. A number …
Starting from constrained Skyrme-mean-field calculations, the low-energy excitation spectrum of 16O is calculated by configuration mixing of particle-number and angular-momentum projected mean-field states in the framework of the Generator Coordinate Method. Without any adjustable parameters, this approach gives a very good description of those states and their transition moments that can be described with our restriction to axially and reflection-symmetric shapes. The structure of low-lying 0+ states is analyzed in terms of self-consistent 0p-0h, 2p-2h, and 4p-4h Hartree-Fock states.
The ground-state properties of 64Ge, 68Se, 72Kr and 76Sr (N=Z) nuclei have been investigated by using Hartree-Fock-Bogolibov (HFB)method with Sly4 Skyrme forces and Relativistic Mean Field (RMF) model with NL3 and recently proposed DEFNE interaction parameters sets. For determination of ground-state axially deformed shape and quadrupole moment constrained calculations have been employed in RMF model. The results of the present study have been compared with each other and available experimental data in the literature. The ground-state binding energies,neutron, proton and charge radii, quadrupol…
We calculate the binding energy, root-mean-square radius and quadrupole deformation parameter for the recent, possibly discovered superheavey element Z=122, using the axially deformed relativistic mean field (RMF) and non-relativistic Skyrme Hartree-Fock (SHF) formalisms. The calculation is extended to include various isotopes of Z=122 element, strarting from A=282 to A=320. We predict highly deformed structures in the ground state for all the isotopes. A shape transition appears at about A=290 from a highly oblate to a large prolate shape, which may be considered as the superdeformed and hype…
We study the shape of $Λ$ hypernuclei in the full ($β,γ$) deformation plane, including both axially symmetric and triaxial quadrupole deformations. To this end, we use the constrained Skyrme Hartree-Fock+BCS method on the three-dimensional Cartesian mesh. The potential energy surface is analyzed for carbon hypernuclei as well as for sd-shell hypernuclei such as $^{27,29}_Λ$Si and $^{25,27}_Λ$Mg. We show that the potential energy surface in the ($β,γ$) plane is similar to each other between the hypernuclei and the corresponding core nuclei, although the addition of $Λ$ hyperon makes the energy …
Ground and isomeric states of the neutron-deficient odd-$A$ isotopes $^{183}$Hg, $^{185}$Hg, and $^{187}$Hg are described from a microscopic calculation based on a self-consistent, axially-deformed Hartree-Fock mean field with the Skyrme functional and pairing within BCS approximation. For each equilibrium shape and different odd-neutron states, results on mean square charge radii and magnetic dipole moments are given and analyzed in the context of their sensitivity to the nuclear deformation and to the spin and parity. Spin-isospin correlations within proton-neutron quasiparticle random phase…
The structures of He and Be even-even isotopes are investigated using an axially symmetric Hartree-Fock approach with a Skyrme-IIIls mean field potential. In these simple HF calculations, He and Be isotopes appear to be prolate in their ground states and Be isotopes have oblate shape isomeric states. It is also shown that there exists a level crossing when the nuclear shape changes from the prolate state to the oblate state. The single neutron levels of Be isotopes exhibit a neutron magic number 6 instead of 8 and show that the level inversion between 1/2- and 1/2+ levels occurs only for a lar…
We have developed a new Hartree-Fock-Bogoliubov (HFB) code which has been specifically designed to study ground state properties of nuclei near the neutron and proton drip lines. The unique feature of our code is that it takes into account the strong coupling to high-energy continuum states, up to an equivalent single-particle energy of 60 MeV. We solve the HFB equations for deformed, axially symmetric even-even nuclei in coordinate space on a 2-D lattice with Basis-Spline methods. For the p-h channel, the Skyrme (SLy4) effective N-N interaction is utilized, and for the p-p and h-h channel we …
Shape-phase transition in neutron-rich Cr isotopes around N=40 is investigated by employing the collective Hamiltonian approach. The inertial functions for large-amplitude vibration and rotation are evaluated by the local normal modes along the axial quadrupole collective coordinate using the Skyrme and pairing energy density functionals. The time-odd components of the mean fields are fully included in the derived masses. The low-lying spectra obtained by requantizing the collective Hamiltonian show an excellent agreement with the recent experimental data. Gradual change from spherical to axia…
The ground state and first intrinsic excited state of superheavy nuclei with Z=120 and N=160-204 are investigated using both non-relativistic Skyrme-Hartree-Fock and the axially deformed Relativistic Mean Field formalisms. We employ a simple BCS pairing approach for calculating the energy contribution from pairing interaction. The results for isotopic chain of binding energy, quadrupole deformation parameter, two neutron separation energies and some other observables are compared with the FRDM and some recent macroscopic-microscopic calculations. We predict superdeformed ground state solutions…
The systematic study of isoscalar (IS) and isovector (IV) giant quadrupole responses (GQR) in normal and superfluid nuclei presented in [G. Scamps and D. Lacroix, Phys. Rev. 88, 044310 (2013)] is extended to the case of axially deformed and triaxial nuclei. The static and dynamical energy density functional based on Skyrme effective interaction are used to study static properties and dynamical response functions over the whole nuclear chart. Among the 749 nuclei that are considered, 301 and 65 are respectively found to be prolate and oblate while 54 do not present any symmetry axis. For these …
Two-neutron transfer reactions are studied within the interacting boson model based on the nuclear energy density functional theory. Constrained self-consistent mean-field calculations with the Skyrme energy density functional are performed to provide microscopic input to completely determine the Hamiltonian of the IBM. Spectroscopic properties are calculated only from the nucleonic degrees of freedom. This method is applied to study the $(t,p)$ and $(p,t)$ transfer reactions in the assorted set of rare-earth nuclei $^{146-158}$Sm, $^{148-160}$Gd, and $^{150-162}$Dy, where spherical-to-axially…
Modelling fission with microscopic input: excitation-energy-dependent fission paths for neutron-induced reactions
Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles（布鲁塞尔天文与天体物理研究所，布鲁塞尔自由大学）；Brussels Laboratory of the Universe - BLU-ULB（宇宙布鲁塞尔实验室）
