Hartree Fock Bogoliubov Method Research Articles

Single Folding Potential Calculations in 141Pr

In this study, Skyrme and Gogny forces have been used to describe interactions for Hartree-Fock (HF) and Hartree-Fock-Bogoliubov (HFB) calculations, considering all nucleons to evaluate nucleon densities. The nucleon densities of the 141Pr were calculated by using the Skyrme-HF (SHF) method with Woods-Saxon Potential (SHF-WS) and with Harmonic Oscillator Potential (SHF-HO), HFB method with Skyrme (HFB-S) and with Gogny (HFB-G) interactions. In these calculations, the effects of the three-body force have been accounted for in both Skyrme and Gogny forces through a density-dependent term necessary to describe various properties of nuclei and nuclear matter. The root-mean-square (rms) radii of proton, neutron, and charge densities of the nucleus were calculated using the density-dependent Skyrme-type effective nucleon-nucleon (NN) interaction in the HF approach. The Folding potential, developed to describe nucleon-nucleus (n-Pr) elastic scattering data, was obtained by single folding potential to calculate reaction cross-section calculations for 141Pr target. The calculated cross-sections, obtained using density data from four different models, were compared with each other and with experimental data from the literature for analysis and interpretation of the results.

A novel approach for taking into account the zero-point oscillations in calculating heavy-ion fusion cross-sections

Earlier in the literature it was shown that accounting for the zero-point oscillations (ZPO) of the shape of colliding atomic nuclei results in significant increasing of the calculated sub-barrier capture (fusion) crosssections. However, calculations of such kind were performed in a simplified way with the schematic nucleus– nucleus potential. The purpose of the present paper is to estimate in an accurate way the sub-barrier capture cross-sections in collisions between oxygen-16 and spherical nuclei with the realistic potential and to compare the calculated cross-sections with the experimental data. Nucleus-nucleus potential is obtained within the doublefolding model with Paris M3Y nucleon–nucleon effective forces. The nucleon densities are taken from the IAEA data base (they are calculated using the Hartree–Fock–Bogoliubov method and approximated by two-parameter Fermi profile). The transmission coefficients are calculated within the WKB approximation below the Coulomb barrier and within parabolic barrier approximation above it. A novel approach for taking into account the ZPO without any fitting parameters is proposed. It is demonstrated that ignoring the ZPO results in underestimating the experimental data whereas accounting for ZPO improves the agreement of the calculated cross-sections with the experimental ones.

Time-dependent Hartree–Fock–Bogoliubov method for molecular systems: An alternative excited-state methodology including static electron correlation

TheHartree–Fock–Bogoliubov (HFB) method, an efficient way to treat static electron correlations, has been applied to molecular systems in the ground state. In this letter, we propose a time-dependent (TD) HFB method for treating the excited states of molecules with static correlations at a reasonable computational cost. To avoid electron number violations, we also consider the canonical basis variant of the TDHFB method proposed by Ebata et al. Results of calculations for the elongated hydrogen molecule reveal that the TDHFB method can partially incorporate two-electron excited determinants.

Self-consistent description of Bose–Bose droplets: modified gapless Hartree–Fock–Bogoliubov method

We define a formalism of a self-consistent description of the ground state of a weakly interacting Bose system, accounting for higher order terms in expansion of energy in the diluteness parameter. The approach is designed to be applied to a Bose–Bose mixture in a regime of weak collapse where quantum fluctuations lead to stabilization of the system and formation of quantum liquid droplets. The approach is based on the generalized Gross–Pitaevskii equation accounting for quantum depletion and renormalized anomalous density terms. The equation is self-consistently coupled to modified Bogoliubov equations. We derive well defined procedure to calculate the zero temperature renormalized anomalous density—the quantity needed to correctly describe the formation of quantum liquid droplet. We pay particular attention to the case of droplets harmonically confined in some directions. The method allows to determine the Lee–Huang–Yang-type contribution to the chemical potential of inhomogeneous droplets when the local density approximation fails.

Proton radioactivity and α-decay of neutron-deficient nuclei

Proton radioactivity and α-decay half-lives of neutron-deficient nuclei have been systematically studied. The proton-nucleus interaction potential is developed by single folding the density distribution of the daughter nuclei with the effective M3Y-Paris nucleon-nucleon (NN) interaction. The penetrability is calculated with the Wentzel-Kramers-Brillouin approximation. The applicability of the universal decay law on the proton decay half-lives has been examined and a new set of parameters has been identified. The competition between α-decay and proton radioactivity of neutron-deficient nuclei has been investigated. The proton radioactivity is found to be the dominant mode of decay for nuclides located very close to the proton drip-line. The effect of using different microscopic proton and neutron density distributions on the half-lives for these two decay modes is studied. It is found that the calculated half-lives with the microscopic densities that obtained from the self-consistent Hartree–Fock-Bogoliubov method successfully reproduce the experimental data. The impact of nuclear deformation on the half-lives is investigated for these two decay modes. The influence of nonlocality through the finite-range exchange part of the NN interaction on the α-decay process is elucidated. Our theoretical calculations have been confirmed experimentally and satisfactory agreement has been achieved.

Investigation of the magicity in some even–even Ca isotopes by using shell model and Hartree–Fock–Bogoliubov method

In the present work, the bulk nuclear properties and features of some of the excited states in the neutron-rich even–even 46−54Ca isotopes have been investigated. In order to identify the magicity and the existence of new magic numbers in these isotopes, the shell model and Hartree–Fock–Bogoliubov method were implemented based on Skyrme parameterizations. In particular, root-mean-square charge radius, binding energies, one- and two-neutron separation energies, pairing gaps, reduced transition probabilities, excitation energies, energy levels, and quadrupole deformation parameters have been investigated. The calculated results were compared with available experimental data.

Estimation of Electrical Conductivity and Magnetization Parameter of Neutron Star Crusts and Applied to the High-Braking-Index Pulsar PSR J1640-4631

Young pulsars are thought to be highly magnetized neutron stars (NSs). The crustal magnetic field of a NS usually decays at different timescales in the forms of Hall drift and Ohmic dissipation. The magnetization parameter ω B τ is defined as the ratio of the Ohmic timescale τ O h m to the Hall drift timescale τ H a l l . During the first several million years, the inner temperature of the newly born neutron star cools from T = 10 9 K to T = 1.0 × 10 8 K, and the crustal conductivity increases by three orders of magnitude. In this work, we adopt a unified equations of state for cold non-accreting neutron stars with the Hartree–Fock–Bogoliubov method, developed by Pearson et al. (2018), and choose two fiducial dipole magnetic fields of B = 1.0 × 10 13 G and B = 1.0 × 10 14 G, four different temperatures, T, and two different impurity concentration parameters, Q, and then calculate the conductivity of the inner crust of NSs and give a general expression of magnetization parameter for young pulsars: ω B τ ≃ ( 1 − 50 ) B 0 / ( 10 13 G) by using numerical simulations. It was found when B ≤ 10 15 G, due to the quantum effects, the conductivity increases slightly with the increase in the magnetic field, the enhanced magnetic field has a small effect on the matter in the low-density regions of the crust, and almost has no influence the matter in the high-density regions. Then, we apply the general expression of the magnetization parameter to the high braking-index pulsar PSR J1640-4631. By combining the observed arrival time parameters of PSR J1640-4631 with the magnetic induction equation, we estimated the initial rotation period P 0 , the initial dipole magnetic field B 0 , the Ohm dissipation timescale τ O h m and Hall drift timescale τ H a l l . We model the magnetic field evolution and the braking-index evolution of the pulsar and compare the results with its observations. It is expected that the results of this paper can be applied to more young pulsars.

Investigation of the existence of new nuclear magic number in even-even O isotopes using shell model and Hartree–Fock Bogoliubov method

In the present work, the features of some excited states in some even–even 14-26O isotopes have been investigated. The aim is to predict the evaluated existence of magic numbers in these isotopes using shell model and Hartree-Fock Bogoliubov method based on SLy4, SkC, SkD Skyrme parameterizations. In particular, root mean square radius, binding energies, one and two neutron separation energies, pairing gaps, transition probabilities, excitation energies, energy levels, transition densities and quadrupole deformation parameters have been investigated. The results are compared with the available experimental data.

Study of the nuclear deformation of some even–even isotopes using Hartree–Fock–Bogoliubov method (effect of the collective motion)

In the present research, the nuclear deformation of the Ne, Mg, Si, S, Ar, and Kr even–even isotopes has been investigated within the framework of Hartree–Fock–Bogoliubov method and SLy4 Skyrme parameterization. In particular, the deform shapes of the effect of nucleons collective motion by coupling between the single-particle motion and the potential surface have been studied. Furthermore, binding energy, the single-particle nuclear density distributions, the corresponding nuclear radii, and quadrupole deformation parameter have been also calculated and compared with the available experimental data. From the outcome of our investigation, it is possible to conclude that the deforming effects cannot be neglected in a characterization of the structure of the neutron-rich nuclei. The relation between the single-particle motion and the potential surface leads to note that the change in the interactions between the nucleons causes the evolution of nuclear surface and leads to variation in the potential shape.

Nuclear structure investigation of even–even and odd Pb isotopes by using the Hartree–Fock–Bogoliubov method

The nuclear structure of even–even and odd lead isotopes ([Formula: see text]Pb) is investigated within the Hartree–Fock–Bogoliubov (HFB) theory. Calculations are performed for a wide range of neutron numbers, starting from the proton-rich side up to the neutron-rich side, by using the SLy4 Skyrme interaction and a new proposed formula for the pairing strength which is more precise for this region of nuclei as we did in previous works in the regions of Neodymium (Nd, [Formula: see text]) [Y. El Bassem and M. Oulne, Int. J. Mod. Phys. E 24 (2015) 1550073] and Molybdenum (Mo, [Formula: see text]) [Y. El Bassem and M. Oulne, Nucl. Phys. A 957 (2017) 22]. Such a new pairing strength formula allows reaching exotic nuclei region where the experimental data are not available. Calculated values of various physical quantities such as binding energy, two-neutron separation energy, quadrupole deformation, and rms-radii for protons and neutrons are discussed and compared with experimental data and some estimates of other nuclear models like Finite Range Droplet Model (FRDM), Relativistic Mean Field (RMF) model with NL3 functional (NL3), Density-Dependent Meson-Exchange Relativistic Energy Functional (DD-ME2) and results of HFB calculations based on the D1S Gogny effective nucleon–nucleon interaction (Gogny D1S).

Divide-and-Conquer Hartree–Fock–Bogoliubov Method and Its Application to Conjugated Diradical Systems

The Hartree–Fock–Bogoliubov (HFB) theory has recently attracted considerable attention in quantum chemistry as a novel strategy to account for the static electron correlation, which plays an essent...

Generalized Hartree-Fock-Bogoliubov description of the Fröhlich polaron

We adapt the generalized Hartree-Fock-Bogoliubov (HFB) method to an interacting many-phonon system free of impurities. The many-phonon system is obtained from applying the Lee-Low-Pine (LLP) transformation to the Frohlich model which describes a mobile impurity coupled to noninteracting phonons. We specialize our general HFB description of the Frohlich polaron to Bose polarons in quasi-1D cold atom mixtures. The LLP transformed many-phonon system distinguishes itself with an artificial phonon-phonon interaction which is very different from the usual two-body interaction. We use the quasi-one-dimensional model, which is free of an ultraviolet divergence that exists in higher dimensions, to better understand how this unique interaction affects polaron states and how the density and pair correlations inherent to the HFB method conspire to create a polaron ground state with an energy in good agreement with and far closer to the prediction from Feynman's variational path integral approach than mean-field theory where HFB correlations are absent.

Hartree–Fock–Bogoliubov calculation of ground state properties of even–even and odd Mo and Ru isotopes

In a previous work (El Bassem and Oulne (2015) [20]), hereafter referred to as paper I, we have investigated the ground-state properties of Nd, Ce and Sm isotopes within Hartree–Fock–Bogoliubov method with SLy5 Skyrme force in which the pairing strength has been generalized with a new proposed formula. However, that formula is more appropriate for the region of Nd. In this work, we have studied the ground-state properties of both even–even and odd Mo and Ru isotopes. For this, we have used Hartree–Fock–Bogoliubov method with SLy4 Skyrme force, and a new formula of the pairing strength which is more accurate for this region of nuclei. The results have been compared with available experimental data, the results of Hartree–Fock–Bogoliubov calculations based on the D1S Gogny effective nucleon–nucleon interaction and predictions of some nuclear models such as Finite Range Droplet Model (FRDM) and Relativistic Mean Field (RMF) theory.

Ground state properties of even–even and odd Nd, Ce and Sm isotopes in Hartree–Fock–Bogoliubov method

In this work, we have studied the ground state properties of both even–even and odd Nd isotopes within Hartree–Fock–Bogoliubov method with SLy5 Skyrme force in which the pairing strength has been generalized with a new proposed formula. We calculated binding energies, two-neutron separation energies, quadrupole deformation, charge, neutron and proton radii. Similar calculations have been carried out for Ce and Sm in order to verify the validity of our pairing strength formula. The results have been compared with available experimental data, the results of Hartree–Fock–Bogoliubov calculations based on the D1S Gogny effective nucleon–nucleon interaction and predictions of some nuclear models such as finite range droplet model (FRDM) and relativistic mean field (RMF) theory.

Shape of Te isotopes in mean-field formalism

The systematic investigation of ground state shape evolution from gamma unstable O(6) to spherical U(5) for Te isotopes has been presented by using the quadrupole moment constrained Hartree Fock Bogoliubov (HFB) method with the Skyrme force SLy4. 124Te has been pointed out as to be the possible critical point nucleus with E(5) symmetry.

Gradient of molecular Hartree–Fock–Bogoliubov energy with a linear combination of atomic orbital quasiparticle wave functions

The analytical gradient for the atomic-orbital-based Hartree-Fock-Bogoliubov (HFB) energy functional, the modified form of which was proposed by Staroverov and Scuseria to account for the static electron correlation [J. Chem. Phys. 117, 11107 (2002)], is derived. Interestingly, the Pulay force for the HFB energy is expressed with the same formula as that for the Hartree-Fock method. The efficiency of the present HFB energy gradient is demonstrated in the geometry optimizations of conjugated and biradical systems. The geometries optimized by using the HFB method with the appropriate factor ζ, which controls the degree of static correlation included, are found to show good agreement with those obtained by using a complete active-space self-consistent field method, although they are significantly dependent on ζ.

Nuclear level densities of64,66Zn from neutron evaporation

Double differential cross sections of neutrons from $d\phantom{\rule{0.16em}{0ex}}+{\phantom{\rule{0.16em}{0ex}}}^{63,65}$Cu reactions have been measured at deuteron energies of 6 and 7.5 MeV. The cross sections measured at backward angles have been compared to theoretical calculations in the framework of the statistical Hauser-Feshbach model. Three different level density models were tested: the Fermi-gas model, the Gilbert-Cameron model, and the microscopic approach through the Hartree-Fock-Bogoliubov method (HFBM). The calculations using the Gilbert-Cameron model are in best agreement with our experimental data. Level densities of the residual nuclei ${}^{64}$Zn and ${}^{66}$Zn have been obtained from statistical neutron evaporation spectra. The angle-integrated cross sections have been analyzed with the exciton model of nuclear reaction.

Microscopic mass models for astrophysics

We review the various microscopic mass models based on effective interactions that have been developed in recent years, primarily with a view to extrapolation from the mass data to the highly neutron-rich environments that are encountered in various astrophysical contexts but that are experimentally inaccessible. All these models are based on the Hartree–Fock–Bogoliubov method, and use either Skyrme-type or Gogny-type effective interactions; they are likewise all constrained by many-body calculations on neutron matter with realistic nucleonic interactions.

Finite-temperature analysis of a quasi-two-dimensional dipolar gas

We present finite temperature analysis of a quasi2D dipolar gas. To do this, we use the Hartree Fock Bogoliubov method within the Popov approximation. This formalism is a set of non-local equations containing the dipole-dipole interaction and the condensate and thermal correlation functions, which are solved self-consistently. We detail the numerical method used to implement the scheme. We present density profiles for a finite temperature dipolar gas in quasi2D, and compare these results to a gas with zero-range interactions. Additionally, we analyze the excitation spectrum and study the impact of the thermal exchange.

Effective pairing interactions with isospin density dependence

We perform Hartree-Fock-Bogoliubov (HFB) calculations for semi-magic calcium, nickel, tin, and lead isotopes and $N=20,28,50$, and 82 isotones using density-dependent pairing interactions recently derived from a microscopic nucleon-nucleon interaction. These interactions have an isovector component so that the pairing gaps in symmetric and neutron matter are reproduced. Our calculations well account for the experimental data for the neutron number dependence of binding energy, two-neutron separation energy, and odd-even mass staggering of these isotopes. This result suggests that by introducing the isovector term in the pairing interaction, one can construct a global effective pairing interaction that is applicable to nuclei in a wide range of the nuclear chart. It is also shown with the local density approximation that the pairing field deduced from the pairing gaps in infinite matter reproduces qualitatively well the pairing field for finite nuclei obtained with the HFB method.