Hartree-Fock-Bogoliubov Model Research Articles

Proton and Neutron Pairing Properties within a Mixed Volume-Surface Pairing Type Using the Hartree–Fock–Bogolyubov Theory

This work aims at systematic investigations of the proton and neutron pairing properties and Fermi energies in the region from the proton drip-line to the neutron drip-line. In order to obtain a more accurate mass formula with the Skyrme (SKI3) force, the global descriptive power of the Skyrme–Hartree–Fock–Bogoliubov model for pairing properties is applied. Systematic Skyrme–HFB calculations with a mixed volume-surface pairing are carried out to study the ground-state proton pairing gap, neutron and proton pairing energies, and the neutron and proton Fermi energies for about 2095 even-even nuclei ranging from 2 ≤ Z ≤ 110 to 2 ≤ N ≤ 236 . The calculated values of proton pairing gaps are compared with experimental data, by using the difference-point formulas Δ(3), Δ(4), and Δ(5), and compared with the proton pairing gap in the Lipkin–Nogami model. It is shown that the Skyrme (SKI3) force with the mixed volume-surface pairing can be successfully used for describing the ground-state proton pairing gap, proton and neutron pairing energies, and proton and neutron Fermi properties of the investigated nuclei, in particular, the neutron-rich nuclei and the exotic nuclei near the neutron drip-line. On the other hand, the calculated proton pairing gap shows the acceptable agreement with the available experimental values of the proton pairing gap with the use of the difference-point formulas Δ(3), Δ(4), and Δ(5) and with the data of the Lipkin–Nogami model over the whole nuclear chart.

Prediction of exotic hyperon halos in neutron-rich Zr hypernuclei

Abstract We study the single- and double-Λ hypernuclei in Zr isotopes with the Hartree–Fock–Bogoliubov model and Skyrme-type nucleon–nucleon, Λ–nucleon, and Λ–Λ interactions. We found two peculiar features of the Λ hyperon halo phenomena that have never been found in nuclei without the strangeness degree of freedom. One is the d-wave halo, and the other is a bunch of three halo orbits just below the Λ hyperon threshold in $^{137}_\Lambda$Zr and also in $^{138}_{\Lambda \Lambda }$Zr. We name these exotic halo phenomena giant hyperon halos in hypernuclei whose core nucleus 136Zr was predicted to have a “giant neutron halo.” The interaction between Λ hyperons and the neutrons is responsible for inducing giant hyperon halo phenomena in the single- and double-Λ nuclei $^{137}_\Lambda$Zr and $^{138}_{\Lambda \Lambda }$Zr.

Microscopic study of shape evolution and some important ground state properties of 190–210Au isotopes

In this paper, we have examined the nuclear structural properties of 190–210Au isotopes within the framework of the Hartree–Fock–Bogoliubov Model. For the theoretical calculations, we have used the UNEDF2 and SKP interactions. The studies include the shape evolution, quadrupole deformation parameter [Formula: see text], nuclear electric quadrupole moment Q(b), single-particle energy levels, the binding energy per nucleon, nuclear charge radius, neutron rms radius, proton rms radius and neutron skin thickness. To analyze the accuracy of our theoretical results, we have presented the comparative analysis with experimental data and finite-range droplet model calculations. The adequate resemblance with experimental data is supporting our studies. We observe the oblate-prolate shape coexistence for 190Au, 193Au and 195Au using the UNEDF2 interaction.

Neutrons in the classically forbidden region in neutron-rich nucleus 68Ca * *Supported by China Scholarship Council (201906255002)

Neutrons tunneling to the classically forbidden (CF) region in the neutron-rich nucleus are investigated in the Skyrme Hartree-Fock (HF) and Hartree-Fock-Bogoliubov (HFB) models. The definition of the CF region is examined in the HF model by using different single-particle potentials for the bound states. In the HFB model, the weakly bound and continuum states could also contribute to the neutrons in the CF region due to the pairing correlation. Their asymptotic wave functions are carefully calculated by the Green’s function method.

Microscopic study of shape evolution and ground-state properties of Iodine isotopes

In this paper, we investigated the shape evolution and ground-state properties of 108−144I isotopes using Hartree–Fock-Bogoliubov Model while employing the axially deformed single-particle harmonic oscillator basis for the expansion of quasiparticle wave functions. We have used SKP and UNEDF2 models to perform the theoretical calculations. We have presented the shape evolution and final values of the quadrupole deformation parameter β 2 of iodine isotopes. We have used the final values of the β 2 for studying the ground-state properties of the iodine isotopic chain. The investigated ground-state properties are the nuclear electric quadrupole moment, single-particle energy levels, the binding energy per nucleon, pairing energy, one-neutron separation energy, two-neutron separation energy, nuclear charge radius, neutron rms radius, proton rms radius, and neutron skin thickness. After using the SKP parameterization on 109I, we have observed the shape coexistence of prolate and oblate shape. Similarly, after using the UNEDF2 parameterization on 110I, 112I, 114I, 115I, 116I, 117I, 118I, and 119I, we discover the shape coexistence of prolate and oblate shape.

A comparative study of α-decay and spontaneous fission for Z = 120 superheavy isotopes

In this study, we have investigated the [Formula: see text]-decay chains of even–even superheavy nuclei [Formula: see text] in the range of [Formula: see text]. The Hartree–Fock–Bogoliubov model is used to calculate the binding energy of these superheavy nuclei. We have included the so-called SkP skyrme function as an effective force and the quadruple deformations. The semi-empirical formulas are used in the reproducing [Formula: see text]-decay and spontaneous fission half-lives of these superheavy nuclei. By studying the decay chains of the Z = 120 isotopes and comparing them with the half-lives of spontaneous fission, it is predicted that the elements [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text],[Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] are more stable than the neighboring isotopes in their parent [Formula: see text]-decay chain. The corresponding neutron and proton numbers represent magical behavior that is in agreement with the numbers predicted before. In this range, the predicted nuclei are found to have large enough half-lives to synthesize them in a laboratory.

Analysis of neutron capture cross section using different level density models on cadmium isotopes up to 250 keV neutron-induced energy and GEANT4 simulation

The neutron capture cross-sectional reactions for 106,108,110,111,112,113,114,116Cd isotopes have been calculated with different level density models which are constant temperature Fermi gas (CTFG) model, back-shifted Fermi gas model, generalized superfluid model and Hartree–Fock–Bogoliubov model by using TALYS 1.9 and EMPIRE 3.2 codes for incident neutron energies up to 250 keV. The obtained results have been analyzed with each level density model parameters existing in Reference Input Parameter Library (RIPL-3) and available experimental data. As an outcome, to obtain more precise and coherent calculations with the experimental values, level density model and its parameters have been determined. Also, hadronic interactions of low-energy neutrons have been investigated for a situation by using GEANT4.

Fission fragment mass yield deduced from density distribution in the pre-scission configuration

Static self-consistent methods usually allow one to determine the most probable fission fragments mass asymmetry. We have applied random neck rupture mechanism to the nuclei in the configuration at the end of fission paths. Fission fragment mass distributions have been deduced from the pre-scission nuclear density distribution obtained from the self-consistent calculations. Potential energy surfaces as well as nuclear shapes have been calculated in the fully microscopic theory, namely the constrained Hartree–Fock–Bogoliubov model with the effective Gogny D1S density-dependent interaction. The method has been applied for analysis of fission of Fm, 252Cf and 180Hg and compared with the experimental data.

Description of the ground state of axially deformed nuclei within the Relativistic Hartree–Fock–Bogoliubov model

The Relativistic Hartree–Fock–Bogoliubov model for axially deformed nuclei (RHFBz) is presented. The model involves a phenomenological Lagrangian with density-dependent meson–nucleon couplings in the particle-hole channel and the central part of the Gogny force in the particle–particle channel. The RHFBz equations are solved by expansion in the basis of a deformed harmonic oscillator. Illustrative RHFBz calculations are performed for Neon isotopes.

On Blowup for Time-Dependent Generalized Hartree–Fock Equations

We prove finite-time blowup for spherically symmetric and negative energy solutions of Hartree–Fock and Hartree–Fock–Bogoliubov-type equations, which describe the evolution of attractive fermionic systems (e.g. white dwarfs). Our main results are twofold: first, we extend the recent blowup result of Hainzl and Schlein (Comm. Math. Phys. 287:705–714, 2009) to Hartree–Fock equations with infinite rank solutions and a general class of Newtonian type interactions. Second, we show the existence of finite-time blowup for spherically symmetric solutions of a Hartree–Fock–Bogoliubov model, where an angular momentum cutoff is introduced. We also explain the key difficulties encountered in the full Hartree–Fock–Bogoliubov theory.

Minimizers for the Hartree-Fock-Bogoliubov theory of neutron stars and white dwarfs

We prove the existence of minimizers for Hartree-Fock-Bogoliubov (HFB) energy functionals with attractive two-body interactions given by Newtonian gravity. This class of HFB functionals serves as a model problem for self-gravitating relativistic Fermi systems, which are found in neutron stars and white dwarfs. Furthermore, we derive some fundamental properties of HFB minimizers such as a decay estimate for the minimizing density. A decisive feature of the HFB model in gravitational physics is its failure of weak lower semicontinuity. This fact essentially complicates the analysis compared to the well-studied Hartree-Fock theories in atomic physics

Boundary Conditions of Wigner-Seitz Cell in Inner Crust of Neutron Stars with Relativistic Mean Field Approach

The microscopic structure of the Wigner–Seitz (W-S) cell in the inner crust of neutron stars is investigated with the relativistic mean field (RMF) approach. The W-S cell is composed of a cluster of neutrons and protons localized in a region around the centre and surrounded by a neutron gas of approximately uniform density. In order to generate the density of the W-S cell, appropriate boundary conditions in the calculation of the single-particle wavefunctions are necessary. We emphasize on the choice of the boundary conditions in the RMF approach. Three kinds of boundary conditions are suggested. The properties of the W-S cell with the three kinds of boundary conditions are investigated. The neutron density distributions in the RMF and Hartree–Fock–Bogoliubov (HFB) models are compared. It is found that the neutron gas densities of the W-S cell in the RMF model is higher than those obtained in the HFB model.