Evaluation of Suitable Mean-Field (Hartree-Fock) Representations for Perturbational Studies of Disordered Solids

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.

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RELATIVE MOTION CORRECTION TO FISSION BARRIERS

International Journal of Modern Physics E ◽

10.1142/s0218301308009641 ◽

2008 ◽

Vol 17 (01) ◽

pp. 151-159 ◽

Cited By ~ 5

Author(s):

J. SKALSKI

Keyword(s):

Relative Motion ◽

Cluster Model ◽

Motion Correction ◽

Mean Field Theory ◽

Mean Field ◽

Ternary Fission ◽

Skyrme Interaction ◽

Hartree Fock ◽

Fission Barriers ◽

The Mean

We discuss the effect of kinetic energy of the relative motion becoming spurious for separate fragments on the selfconsistent mean-field fission barriers. The treatment of the relative motion in the cluster model is contrasted with the necessity of a simpler and approximate approach in the mean-field theory. A scheme of the energy correction to the Hartree-Fock is proposed. The results obtained with the effective Skyrme interaction SLy 6 show that the correction, previously estimated as ~ 8 MeV in A = 70 - 100 nuclei, amounts to 4 MeV in the medium heavy nucleus 198 Hg and to null in 238 U . However, the corrected barrier implies a shorter fission half-life of the latter nucleus. The same effect is expected to lower barriers for multipartition (i.e. ternary fission, etc) and make hyperdeformed minima less stable.

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Investigation of the nuclear structure of 84-108Mo isotopes using Skyrme-Hartree-Fock method

Iraqi Journal of Physics (IJP) ◽

10.30723/ijp.v13i26.278 ◽

2019 ◽

Vol 13 (26) ◽

pp. 1-11

Author(s):

Ali A. Alzubadi

Keyword(s):

Density Functional ◽

Good Description ◽

Mean Field ◽

Nucleon Nucleon ◽

Effective Density ◽

Skin Thickness ◽

Neutron Skin ◽

Energy Density Functional ◽

Charge Densities ◽

Hartree Fock

Over the last few decades the mean field approach using selfconsistentHaretree-Fock (HF) calculations with Skyrme effectiveinteractions have been found very satisfactory in reproducingnuclear properties for both stable and unstable nuclei. They arebased on effective energy-density functional, often formulated interms of effective density-dependent nucleon–nucleon interactions.In the present research, the SkM, SkM*, SI, SIII, SIV, T3, SLy4,Skxs15, Skxs20 and Skxs25 Skyrme parameterizations have beenused within HF method to investigate some static and dynamicnuclear ground state proprieties of 84-108Mo isotopes. In particular,the binding energy, proton, neutron, mass and charge densities andcorresponding root mean square radius, neutron skin thickness andcharge form factor are calculated by using this method with theSkyrme parameterizations mentioned above. The calculated resultsare compared with the available experimental data. Calculationsshow that the Skyrme–Hartree–Fock (SHF) theory with aboveforce parameters provides a good description on Mo isotopes.

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Low-Cost Molecular Excited States from a State-Averaged Resonating Hartree-Fock Approach

10.26434/chemrxiv.7871504 ◽

2019 ◽

Author(s):

Jacob Nite ◽

Carlos A. Jimenez-Hoyos

Keyword(s):

Excited States ◽

Configuration Interaction ◽

Low Cost ◽

Computational Cost ◽

Mean Field ◽

Chem Phys ◽

Spin Projection ◽

Excitation Energies ◽

Hartree Fock ◽

Orbital Relaxation

Quantum chemistry methods that describe excited states on the same footing as the ground state are generally scarce. In previous work, Gill et al. (J. Phys. Chem. A 112, 13164 (2008)) and later Sundstrom and Head-Gordon (J. Chem. Phys. 140, 114103 (2014)) considered excited states resulting from a non-orthogonal configuration interaction (NOCI) on stationary solutions of the Hartree–Fock equations. We build upon those contributions and present the state-averaged resonating Hartree–Fock (sa-ResHF) method, which differs from NOCI in that spin-projection and orbital relaxation effects are incorporated from the onset. Our results in a set of small molecules (alanine, formaldehyde, acetaldehyde, acetone, formamide, and ethylene) suggest that sa-ResHF excitation energies are a notable improvement over configuration interaction singles (CIS), at a mean-field computational cost. The orbital relaxation in sa-ResHF, in the presence of a spin-projection operator, generally results in excitation energies that are closer to the experimental values than the corresponding NOCI ones.

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Low-Cost Molecular Excited States from a State-Averaged Resonating Hartree-Fock Approach

10.26434/chemrxiv.7871504.v1 ◽

2019 ◽

Author(s):

Jacob Nite ◽

Carlos A. Jimenez-Hoyos

Keyword(s):

Excited States ◽

Configuration Interaction ◽

Low Cost ◽

Computational Cost ◽

Mean Field ◽

Chem Phys ◽

Spin Projection ◽

Excitation Energies ◽

Hartree Fock ◽

Orbital Relaxation

Quantum chemistry methods that describe excited states on the same footing as the ground state are generally scarce. In previous work, Gill et al. (J. Phys. Chem. A 112, 13164 (2008)) and later Sundstrom and Head-Gordon (J. Chem. Phys. 140, 114103 (2014)) considered excited states resulting from a non-orthogonal configuration interaction (NOCI) on stationary solutions of the Hartree–Fock equations. We build upon those contributions and present the state-averaged resonating Hartree–Fock (sa-ResHF) method, which differs from NOCI in that spin-projection and orbital relaxation effects are incorporated from the onset. Our results in a set of small molecules (alanine, formaldehyde, acetaldehyde, acetone, formamide, and ethylene) suggest that sa-ResHF excitation energies are a notable improvement over configuration interaction singles (CIS), at a mean-field computational cost. The orbital relaxation in sa-ResHF, in the presence of a spin-projection operator, generally results in excitation energies that are closer to the experimental values than the corresponding NOCI ones.

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Beyond the time-dependent Hartree-Fock: The collision terms in a mean-field theory

Time-Dependent Hartree-Fock and Beyond - Lecture Notes in Physics ◽

10.1007/3-540-11950-7_14 ◽

2008 ◽

pp. 172-180

Author(s):

H.C. Pauli

Keyword(s):

Field Theory ◽

Mean Field Theory ◽

Mean Field ◽

Time Dependent ◽

Hartree Fock

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Comparison between the Thomas–Fermi and Hartree–Fock–Bogoliubov Methods in the Inner Crust of a Neutron Star: The Role of Pairing Correlations

Universe ◽

10.3390/universe6110206 ◽

2020 ◽

Vol 6 (11) ◽

pp. 206

Author(s):

Matthew Shelley ◽

Alessandro Pastore

Keyword(s):

Neutron Star ◽

Mean Field ◽

Pairing Correlation ◽

Field Methods ◽

Density Region ◽

Thomas Fermi ◽

Hartree Fock ◽

Pairing Correlations ◽

Mean Field Methods

We investigated the role of a pairing correlation in the chemical composition of the inner crust of a neutron star with the extended Thomas–Fermi method, using the Strutinsky integral correction. We compare our results with the fully self-consistent Hartree–Fock–Bogoliubov approach, showing that the resulting discrepancy, apart from the very low density region, is compatible with the typical accuracy we can achieve with standard mean-field methods.

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NEUTRON–PROTON PAIRING CORRELATION FOR THE ROTATIONAL MOTION OF N = Z72Kr, 76Sr, AND 80Zr NUCLEI

International Journal of Modern Physics E ◽

10.1142/s0218301311019568 ◽

2011 ◽

Vol 20 (08) ◽

pp. 1687-1699

Author(s):

PRIANKA ROY ◽

SHASHI K. DHIMAN

Keyword(s):

Effective Interaction ◽

Mean Field ◽

High Spin State ◽

Pairing Correlation ◽

Effective Interactions ◽

Hartree Fock ◽

Self Consistent ◽

The Mean ◽

Proton Pairing ◽

Band Crossing

The high-spin state properties of the neutron–proton (np) residual effective interaction are analyzed in N = Z72 Kr , 76 Sr , and 80 Zr nuclei. The self-consistent microscopic Hartree–Fock–Bogoliubov (HFB) equations have been solved by employing monopole corrected two-body effective interaction. A band crossing is observed in 72 Kr nucleus at J = 14ℏ state with monopole corrected "HPU1" and "HPU2" effective interactions. The VAP–HFB theory suggests that the "4p–4h" excitations by np residual interaction are the essential ingredients of the mean-field description of the occurence of backbending in 72 Kr nucleus.

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NUCLEON DISTRIBUTIONS AT NUCLEAR PERIPHERY

Modern Physics Letters A ◽

10.1142/s0217732302006278 ◽

2002 ◽

Vol 17 (19) ◽

pp. 1215-1225

Author(s):

Y. K. GAMBHIR ◽

A. A. BHAGWAT

Keyword(s):

Asymptotic Behavior ◽

Nuclear Periphery ◽

Mean Field ◽

Low Energy ◽

Nucleon Density ◽

Hartree Fock ◽

Density Distributions ◽

Good Account ◽

Density Radius ◽

Density Results

The experimental ratios of the neutron to the proton densities at the nuclear periphery (≃ half-density radius + 2.5 fm) determined using very low energy anti-proton annihilation studies are compared with the predictions of the semi-phenomenological model of the nucleon density distributions. The model incorporates correctly two physical requirements: the correct asymptotic behavior (r → ∞) and the behavior near the center (r → 0). The model gives a good account of the experiment. The results of the more sophisticated, microscopic mean field calculations like non-relativistic Hartree–Fock–Bogoliubov (HFB) with Skyrme type interactions though are qualitatively similar, the model density results are relatively closer to the experiment.

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QUASILOCAL DENSITY FUNCTIONAL THEORY FOR NUCLEI INCLUDING PAIRING CORRELATIONS

International Journal of Modern Physics E ◽

10.1142/s0218301307005697 ◽

2007 ◽

Vol 16 (02) ◽

pp. 249-262 ◽

Cited By ~ 1

Author(s):

X. VIÑAS ◽

V. I. TSELYAEV ◽

V. B. SOUBBOTIN ◽

S. KREWALD

Keyword(s):

Density Functional Theory ◽

Density Functional ◽

Equations Of Motion ◽

Mean Field ◽

Field Operator ◽

Functional Theory ◽

Hartree Fock ◽

Orbit Potential ◽

The Density Functional Theory ◽

Pairing Correlations

We propose first a generalization of the Density Functional Theory leading to single-particle equations of motion with a quasilocal mean-field operator containing a position-dependent effective mass and a spin-orbit potential. Ground-state properties of doubly magic nuclei are obtained within this framework using the Gogny D1S force and compared with the exact Hartree-Fock values. Next, extend the Density Functional Theory to include pairing correlations without formal violation of the particle-number condition. This theory, which is nonlocal, is simplified by a suitable quasilocal reduction. Some calculations to show the ability of this theory are presented.

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