Skyrme–Hartree–Fock–Bogoliubov Calculations of Even and Odd Neutron-Rich Mg Isotopes

2021 ◽  
Vol 66 (11) ◽  
pp. 928
Author(s):  
A.H. Taqi ◽  
M.A. Hasan
Keyword(s):  
Experimental Data ◽  
Mean Field ◽  
Field Method ◽  
Hartree Fock ◽  
Relativistic Mean Field ◽  
Nuclear Models ◽  
Quadrupole Deformation Parameter ◽  
Mg Isotopes ◽  
The One ◽  
Rmf Model

Using the Skyrme functional with SIII, SKM*, SLy4, and UNE0 sets of parameters and the Hartree–Fock–Bogoliubov mean-field method; the ground-state properties of even-even and even-odd neutron-rich Mg isotopes have been investigated. The results of calculations of the binding energy per nucleon (B/A), the one- and two-neutron separation energies (Sn and S2n), proton and neutron rms radii, neutron pairing gap, and quadrupole deformation parameter (B2) have been compared with the available experimental data, the results of Hartree–Fock–Bogoliubov calculations based on the D1S Gogny force, and predictions of some nuclear models such as the Finite Range Droplet Model (FRDM) and Relativistic Mean-Field (RMF) model. Our results show good agreements in comparison with the experimental data and the results of the mentioned models.

THE INNER CRUST OF NEUTRON STARS IN RELATIVISTIC MEAN FIELD APPROACH

2008 ◽  
Vol 17 (09) ◽  
pp. 1765-1773 ◽  
Author(s):  
JIGUANG CAO ◽  
ZHONGYU MA ◽  
NGUYEN VAN GIAI
Keyword(s):  
Boundary Conditions ◽  
Neutron Stars ◽  
Mean Field ◽  
Bcs Theory ◽  
Neutron Density ◽  
Field Approach ◽  
Hartree Fock ◽  
Relativistic Mean Field ◽  
Density Distributions ◽  
Rmf Model

The microscopic properties and superfluidity of the inner crust in neutron stars are investigated in the framework of the relativistic mean field(RMF) model and BCS theory. The Wigner-Seitz(W-S) cell of inner crust is composed of neutron-rich nuclei immersed in a sea of dilute, homogeneous neutron gas. The pairing properties of nucleons in the W-S cells are treated in BCS theory with Gogny interaction. In this work, we emphasize on the choice of the boundary conditions in the RMF approach and superfluidity of the inner crust. Three kinds of boundary conditions are suggested. The properties of the W-S cells with the three kinds of boundary conditions are investigated. The neutron density distributions in the RMF and Hartree-Fock-Bogoliubov(HFB) models are compared.

Properties of Relativistic Mean-Field Theory

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Mean Field Theory ◽  
Mean Field ◽  
Field Method ◽  
Basis Sets ◽  
Electron Interaction ◽  
Relativistic Mean Field ◽  
Dirac Equations ◽  
Electrons And Positrons ◽  
The One ◽  
Atomic Structure Calculations

We have previously seen how the Dirac equation for one particle requires some rather special consideration and interpretation in order to arrive at a form that is able to treat electrons and positrons on an equal footing. These problems persist also when we go to systems with more than one electron. One might think that the extension to several electrons should not introduce dramatic changes. After all, we noted that even the one-electron problem must be viewed as a many-electron (and -positron) system in order to arrive at a consistent description. The problem with introducing more electrons is that electron–electron interactions that were previously small—for the one-electron case typically arising from vacuum polarization and self-interaction—now occur to the same order as the kinetic energy and the interaction with the potential. So while a perturbative approach such as QED can use the solutions of the one-electron Dirac equations as a very good starting approximation to a more accurate description of the full system, the same would not work for a system with more electrons because it would mean neglecting interactions of the same magnitude as the zeroth-order energy. For applications to quantum chemistry, the treatment of the entire electron–electron interaction as a perturbation would be hopelessly impractical, as it is even in manyelectron relativistic atomic structure calculations. The technique for dealing with this problem is well known from nonrelativistic calculations on many-electron systems. One-particle basis sets are developed by considering the behavior of the single electron in the mean field of all the other electrons, and while this neglects a smaller part of the interaction energy, the electron correlation, it provides a suitable starting point for further variational or perturbational treatments to recover more of the electron–electron interaction. It is only natural to pursue the same approach for the relativistic case. Thus one may proceed to construct a mean-field method that can be used as a basis for the perturbation theory of QED.

scholarly journals STRUCTURE EFFECT ON ONE-NEUTRON REMOVAL REACTION USING RELATIVISTIC MEAN FIELD DENSITIES IN GLAUBER MODEL

2011 ◽  
Vol 20 (12) ◽  
pp. 2505-2519 ◽  
Author(s):  
R. N. PANDA ◽  
S. K. PATRA
Keyword(s):  
Experimental Data ◽  
Cross Sections ◽  
Mean Field ◽  
Reaction Cross ◽  
Glauber Model ◽  
Halo Nuclei ◽  
Relativistic Mean Field ◽  
The Difference ◽  
The One ◽  
Good Agreement

We calculate the one-neutron removal reaction cross-section (σ-1n) for a few stable and neutron-rich Boron and Carbon halo nuclei with 12 C as target, using relativistic mean field (RMF) densities, in the frame work of Glauber model. The results are compared with the experimental data. Study of the stable nuclei with the deformed densities have shown a good agreement with the data. However, it differs significantly for the halo nuclei. We observe that while estimating the σ-1n value from the difference of reaction cross-sections of two neighboring nuclei with mass number A and that of A-1 in an isotopic chain, we get good agreement with the known experimental data for the halo cases.

PROPERTIES OF Z = 120 NUCLEI AND THE α-DECAY CHAINS OF THE 292, 304120 ISOTOPES USING RELATIVISTIC AND NONRELATIVISTIC FORMALISMS

2012 ◽  
Vol 21 (11) ◽  
pp. 1250092 ◽  
Author(s):  
SHAKEB AHMAD ◽  
M. BHUYAN ◽  
S. K. PATRA
Keyword(s):  
Excited State ◽  
Ground State ◽  
Half Life ◽  
Mean Field ◽  
Neutron Number ◽  
Α Decay ◽  
Hartree Fock ◽  
Relativistic Mean Field ◽  
Quadrupole Deformation Parameter ◽  
Almost All

The ground state and first intrinsic excited state of superheavy nuclei with Z = 120 and N = 160–204 are investigated using both nonrelativistic Skyrme–Hartree–Fock (SHF) and the axially deformed relativistic mean field (RMF) formalisms. We employ a simple BCS pairing approach for calculating the energy contribution from pairing interaction. The results for isotopic chain of binding energy (BE), quadrupole deformation parameter, two neutron separation energies and some other observables are compared with the finite range droplet model (FRDM) and some recent macroscopic–microscopic calculations. We predict superdeformed ground state solutions for almost all the isotopes. Considering the possibility of magic neutron number, two different modes of α-decay chains 292120 and 304120 are also studied within these frameworks. The Qα-values and the half-life [Formula: see text] for these two different modes of decay chains are compared with FRDM and recent macroscopic–microscopic calculations. The calculation is extended for the α-decay chains of 292120 and 304120 from their excited state configuration to respective configuration, which predicts long half-life [Formula: see text] (in seconds).

scholarly journals ENERGY SYSTEMATICS OF HEAVY NUCLEI — MEAN FIELD MODELS IN COMPARISON

2011 ◽  
Vol 20 (06) ◽  
pp. 1379-1390 ◽  
Author(s):  
P.-G. REINHARD ◽  
B. K. AGRAWAL
Keyword(s):  
Mean Field ◽  
Binding Energies ◽  
Superheavy Nuclei ◽  
Heavy Nuclei ◽  
Hartree Fock ◽  
Relativistic Mean Field ◽  
Mean Field Models ◽  
Opposite Trend ◽  
Super Heavy Nuclei ◽  
Rmf Model

We compare the systematics of binding energies computed within the standard and extended versions of the relativistic mean-field (RMF) model and the Skyrme–Hartree–Fock (SHF) model. The general trends for the binding energies for super-heavy nuclei are significantly different for these models. The SHF models tend to underbind the superheavy nuclei, while RMF models show just the opposite trend. The extended RMF model seems to provide remarkable improvements over the results obtained for the standard RMF model.

scholarly journals Relativistic density functional for nuclear matter

2019 ◽  
Vol 204 ◽  
pp. 05001
Author(s):  
Stefan Gmuca ◽  
Kristian Petrík ◽  
Jozef Leja
Keyword(s):  
Energy Density ◽  
Nuclear Matter ◽  
Density Functional ◽  
Mean Field ◽  
Dense Matter ◽  
Coupling Constants ◽  
Effective Coupling ◽  
Hartree Fock ◽  
Relativistic Mean Field ◽  
Rmf Model

In the present work, we have mapped the exchange Fock contributions from the Dirac–Hartree–Fock (DHF) approach for nuclear matter onto the direct Hartree terms. This results in the relativistic mean field (RMF) model with the density dependent couplings. The density dependence of the effective coupling constants thus reflects the exchange correlations. The exchange part of an energy density of the linear DHF model in dense matter is evaluated in a parameter-free closed form and, after the rearrangement of the terms, expressed as density functional.

INSTABILITIES CONSTRAINT AND RELATIVISTIC MEAN FIELD PARAMETRIZATION

2011 ◽  
Vol 20 (01) ◽  
pp. 81-100 ◽  
Author(s):  
A. SULAKSONO ◽  
KASMUDIN ◽  
T. J. BÜRVENICH ◽  
P.-G. REINHARD ◽  
J. A. MARUHN
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Nuclear Matter ◽  
Nonlinear Term ◽  
Mean Field ◽  
Saturation Point ◽  
Relativistic Mean Field ◽  
Finite Nuclei ◽  
Two Parameter ◽  
Rmf Model

Two parameter sets (Set 1 and Set 2) of the standard relativistic mean field (RMF) model plus additional vector isoscalar nonlinear term, which are constrained by a set of criteria20 determined by symmetric nuclear matter stabilities at high densities due to longitudinal and transversal particle–hole excitation modes are investigated. In the latter parameter set, δ meson and isoscalar as well as isovector tensor contributions are included. The effects in selected finite nuclei and nuclear matter properties predicted by both parameter sets are systematically studied and compared with the ones predicted by well-known RMF parameter sets. The vector isoscalar nonlinear term addition and instability constraints have reasonably good effects in the high-density properties of the isoscalar sector of nuclear matter and certain finite nuclei properties. However, even though the δ meson and isovector tensor are included, the incompatibility with the constraints from some experimental data in certain nuclear properties at saturation point and the excessive stiffness of the isovector nuclear matter equation of state at high densities as well as the incorrect isotonic trend in binding the energies of finite nuclei are still encountered. It is shown that the problem may be remedied if we introduce additional nonlinear terms not only in the isovector but also in the isoscalar vectors.

TABLE OF GROUND STATE PROPERTIES OF NUCLEI IN THE RMF MODEL

2013 ◽  
Vol 28 (16) ◽  
pp. 1350068 ◽  
Author(s):  
TUNCAY BAYRAM ◽  
A. HAKAN YILMAZ
Keyword(s):  
Ground State ◽  
Mean Field ◽  
Properties Of Nuclei ◽  
Relativistic Mean Field ◽  
Ground State Properties ◽  
Pairing Correlations ◽  
Ground State Energies ◽  
Rmf Model

The ground state energies, sizes and deformations of 1897 even–even nuclei with 10≤Z ≤110 have been carried out by using the Relativistic Mean Field (RMF) model. In the present calculations, the nonlinear RMF force NL3* recent refitted version of the NL3 force has been used. The BCS (Bardeen–Cooper–Schrieffer) formalism with constant gap approximation has been taken into account for pairing correlations. The predictions of RMF model for the ground state properties of some nuclei have been discussed in detail.

Nuclear structure and α-decay study of Og isotopes

2019 ◽  
Vol 28 (06) ◽  
pp. 1950041 ◽  
Author(s):  
R. R. Swain ◽  
B. B. Sahu ◽  
P. K. Moharana ◽  
S. K. Patra
Keyword(s):  
Heavy Element ◽  
Mean Field ◽  
Parent Nucleus ◽  
Shell Closure ◽  
Force Parameter ◽  
Α Decay ◽  
Relativistic Mean Field ◽  
Energy Formula ◽  
Text Element ◽  
Rmf Model

We have examined the binding energy, root-mean-square radii and two neutrons separation energies for the recently accepted super-heavy element [Formula: see text] established as Og using the axially deformed relativistic mean field (RMF) model with NL3 force parameter set. The calculation is extended to various isotopes of [Formula: see text] element, starting from [Formula: see text] till [Formula: see text]. The most stable isotope is found to be at [Formula: see text]. Also, the [Formula: see text]-decay energy [Formula: see text] and hence the half-lives [Formula: see text] is carried out by taking three different empirical formulae for the [Formula: see text]-decay chains of [Formula: see text] supporting the possible shell closure at daughter nuclei [Formula: see text] and/ or 184 and at parent nucleus of [Formula: see text] with [Formula: see text].

scholarly journals THE α-DECAY CHAINS OF THE 287, 288115 ISOTOPES USING RELATIVISTIC MEAN FIELD THEORY

2011 ◽  
Vol 20 (10) ◽  
pp. 2217-2228 ◽  
Author(s):  
B. K. SAHU ◽  
M. BHUYAN ◽  
S. MAHAPATRO ◽  
S. K. PATRA
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Superheavy Element ◽  
Binding Energies ◽  
Experimental Result ◽  
Relativistic Mean Field Theory ◽  
Α Decay ◽  
Relativistic Mean Field ◽  
Quadrupole Deformation Parameter

We study the binding energy, root-mean-square radius and quadrupole deformation parameter for the synthesized superheavy element Z = 115, within the formalism of relativistic mean field theory. The calculation is dones for various isotopes of Z = 115 element, starting from A = 272 to A = 292. A systematic comparison between the binding energies and experimental data is made.The calculated binding energies are in good agreement with experimental result. The results show the prolate deformation for the ground state of these nuclei. The most stable isotope is found to be 282115 nucleus (N = 167) in the isotopic chain. We have also studied Qα and Tα for the α-decay chains of 287, 288115.

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