scholarly journals A nuclear matter calculation with the tensor-optimized Fermi sphere method with central interaction

2019 ◽  
Vol 2019 (11) ◽  
Author(s):  
T Yamada ◽  
T Myo ◽  
H Toki ◽  
H Horiuchi ◽  
K Ikeda
Keyword(s):  
Correlation Function ◽  
Nuclear Matter ◽  
Matter Wave ◽  
Many Body ◽  
Expansion Theorem ◽  
Fermi Sphere ◽  
Hartree Fock ◽  
Nuclear Matter Density ◽  
Series Type ◽  
The Many

Abstract The tensor-optimized Fermi sphere (TOFS) theory is applied first for the study of the property of nuclear matter using the Argonne V4$^\prime$$NN$ potential. In the TOFS theory, the correlated nuclear matter wave function is taken to be a power-series type of the correlation function $F$, where $F$ can induce central, spin–isospin, tensor, etc. correlations. This expression has been ensured by a linked cluster expansion theorem established in the TOFS theory. We take into account the contributions from all the many-body terms arising from the product of the nuclear matter Hamiltonian $\mathcal{H}$ and $F$. The correlation function is optimally determined in the variation of the total energy of nuclear matter. It is found that the density dependence of the energy per particle in nuclear matter is reasonably reproduced up to the nuclear matter density $\rho \simeq 0.20$ fm$^{-3}$ in the present numerical calculation, in comparison with other methods such as the Brueckner–Hartree–Fock approach.

scholarly journals THE METHOD OF INCREMENTS — A WAVEFUNCTION-BASED AB-INITIO CORRELATION METHOD FOR SOLIDS

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2204-2214 ◽  
Author(s):  
BEATE PAULUS
Keyword(s):  
Experimental Data ◽  
Ab Initio ◽  
Ground State ◽  
Infinite System ◽  
Correlation Energy ◽  
Correlation Method ◽  
Many Body ◽  
Hartree Fock ◽  
The Many ◽  
Good Agreement

The method of increments is a wavefunction-based ab initio correlation method for solids, which explicitly calculates the many-body wavefunction of the system. After a Hartree-Fock treatment of the infinite system the correlation energy of the solid is expanded in terms of localised orbitals or of a group of localised orbitals. The method of increments has been applied to a great variety of materials with a band gap, but in this paper the extension to metals is described. The application to solid mercury is presented, where we achieve very good agreement of the calculated ground-state properties with the experimental data.

Observable Many-Body Effects of the Two-Body Unobservable Potential

1972 ◽  
Vol 50 (14) ◽  
pp. 1614-1618 ◽  
Author(s):  
N. N. Wong ◽  
M. Razavy
Keyword(s):  
Perturbation Theory ◽  
Phase Shift ◽  
Nuclear Matter ◽  
Particle Scattering ◽  
Body System ◽  
Many Body ◽  
Many Body Effects ◽  
Transparent Potential ◽  
The Many

A two-body transparent potential, which produces no observable phase shift in two-particle scattering, is constructed explicitly. This potential is used to calculate the energy of infinite nuclear matter by applying the perturbation theory and its effects on the many-body system are investigated.

EFFECTS OF CORE POLARIZATION AND PAIRING CORRELATIONS ON SOME GROUND-STATE PROPERTIES OF DEFORMED ODD-MASS NUCLEI WITHIN THE HIGHER TAMM–DANCOFF APPROACH

2011 ◽  
Vol 20 (02) ◽  
pp. 252-258 ◽  
Author(s):  
LUDOVIC BONNEAU ◽  
JULIEN LE BLOAS ◽  
PHILIPPE QUENTIN ◽  
NIKOLAY MINKOV
Keyword(s):  
Ground State ◽  
Mean Field ◽  
Energy Difference ◽  
Pair Type ◽  
Many Body ◽  
Hartree Fock ◽  
Ground State Properties ◽  
Pairing Correlations ◽  
The Many ◽  
The Impact

In self-consistent mean-field approaches, the description of odd-mass nuclei requires to break the time-reversal invariance of the underlying one-body hamiltonian. This induces a polarization of the even-even core to which the odd nucleon is added. To properly describe the pairing correlations (in T = 1 and T = 0 channels) in such nuclei, we implement the particle-number conserving Higher Tamm–Dancoff approximation with a residual δ interaction in each isospin channel by restricting the many-body basis to two-particle–two–hole excitations of pair type (nn, pp and np) on top of the Hartree–Fock solution. We apply this approach to the calculation of two ground-state properties of well-deformed nuclei |Tz| = 1 nuclei around 24 Mg and 48 Cr , namely the isovector odd-even binding-energy difference and the magnetic dipole moment, focusing on the impact of pairing correlations.

scholarly journals A hybrid model of Skyrme- and Brueckner-type interactions for neutron star matter

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Soonchul Choi ◽  
Myung-Ki Cheoun ◽  
K S Kim ◽  
Hungchong Kim ◽  
H Sagawa
Keyword(s):  
Neutron Star ◽  
Hybrid Model ◽  
Clear Understanding ◽  
Neutron Skin ◽  
Neutron Star Matter ◽  
Many Body ◽  
Hartree Fock ◽  
Nuclear Incompressibility ◽  
The Many ◽  
Many Body Interactions

Abstract We suggest a hybrid model for neutron star matter to discuss the hyperon puzzle inherent in the 2.0 M$_{\odot}$ of the neutron star. For the nucleon–nucleon ($NN$) interaction, we employ the Skyrme–Hartree–Fock approach based on various Skyrme interaction parameter sets, and take the Brueckner–Hartree–Fock approach for the interactions related to hyperons. For the many-body interactions including hyperons, we make use of the multi-pomeron-exchange model, whose parameters have been adjusted to the data deduced from various hypernuclei properties. For clear understanding of the physics in the hybrid model, we discuss fractional functions of related particles, symmetry energies, and chemical potentials in dense matter. Finally, we investigate the equations of state and mass–radius relation of neutron stars, and show that the hybrid model can properly describe the 2.0 M$_{\odot}$ neutron star mass data with the many-body interaction employed in the hybrid model. Recent tidal deformability data from the gravitational wave observation are also compared to our calculations, especially in terms of the neutron skin of $^{208}$Pb and nuclear incompressibility.

RECENT PROGRESS IN RELATIVISTIC MANY-BODY APPROACH

2006 ◽  
Vol 15 (07) ◽  
pp. 1447-1464 ◽  
Author(s):  
S. F. BAN ◽  
L. S. GENG ◽  
L. LIU ◽  
W. H. LONG ◽  
J. MENG ◽  
...  
Keyword(s):  
Nuclear Matter ◽  
Shell Model ◽  
Recent Progress ◽  
Many Body ◽  
Density Dependent ◽  
Hartree Fock ◽  
Peking University ◽  
Finite Nuclei

The recent progress of the relativistic many-body approach by the group at Peking University will be reviewed. In particular, the adiabatic and configuration-fixed constrained triaxial RMF approaches, triaxial RMF approach with time-odd components, a Shell-model-Like APproach (SLAP), a Reflection ASymmetric RMF (RAS-RMF) approach, and a new relativistic Hartree-Fock (RHF) approach with density-dependent σ, ω, ρ and π meson-nucleon couplings for finite nuclei and nuclear matter, will be highlighted.

Wave-number dependence of the static screening function of an interacting electron gas. I. Lowest-order Hartree–Fock corrections

1970 ◽  
Vol 48 (2) ◽  
pp. 155-165 ◽  
Author(s):  
D. J. W. Geldart ◽  
Roger Taylor
Keyword(s):  
Coulomb Interaction ◽  
Ground State ◽  
Electron Gas ◽  
Perturbation Expansion ◽  
Wave Number ◽  
Many Body ◽  
Hartree Fock ◽  
The Many ◽  
Static Screening ◽  
Zero Frequency

The lowest-order Hartree–Fock contributions to the zero frequency screening function are examined for an interacting electron gas in its ground state. Computational methods are developed to treat singularities associated with the bare coulomb interaction and vanishing energy denominators of the many-body perturbation expansion. Numerical results are given. The wave-number dependence in the intermediate (k ~ kF) range differs considerably from that of previous estimates.

Correlation energy in triplet electronic states. Application of the many-body Rayleigh-Schrödinger perturbation theory in the restricted Roothaan-Hartree-Fock formalism

1981 ◽  
Vol 46 (6) ◽  
pp. 1324-1331 ◽  
Author(s):  
Petr Čársky ◽  
Ivan Hubač
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Correlation Energy ◽  
Electronic States ◽  
Many Body ◽  
Third Order ◽  
Explicit Formulas ◽  
Hartree Fock ◽  
The Many ◽  
Schrödinger Perturbation

Explicit formulas over orbitals are given for the correlation energy in triplet electronic states of atoms and molecules. The formulas were obtained by means of the diagrammatic many-body Rayleigh-Schrodinger perturbation theory through third order assuming a single determinant restricted Roothaan-Hartree-Fock wave function. A numerical example is presented for the NH molecule.

scholarly journals Hartree–Fock and random phase approximation theories in a many-fermion solvable model

2015 ◽  
Vol 30 (36) ◽  
pp. 1550196 ◽  
Author(s):  
Giampaolo Co’ ◽  
Stefano De Leo
Keyword(s):  
Random Phase Approximation ◽  
Random Phase ◽  
Solvable Model ◽  
Phase Approximation ◽  
Many Body ◽  
Hartree Fock ◽  
Ideal System ◽  
The Many ◽  
Effective Theories ◽  
Number Of Particles

We present an ideal system of interacting fermions where the solutions of the many-body Schrödinger equation can be obtained without making approximations. These exact solutions are used to test the validity of two many-body effective approaches, the Hartree–Fock and the random phase approximation theories. The description of the ground state done by the effective theories improves with increasing number of particles.

scholarly journals Impact of chiral hyperonic three-body forces on neutron stars

2019 ◽  
Vol 55 (11) ◽  
Author(s):  
Domenico Logoteta ◽  
Isaac Vidaña ◽  
Ignazio Bombaci
Keyword(s):  
Neutron Star ◽  
Equation Of State ◽  
Neutron Stars ◽  
Nucleon Nucleon ◽  
Effective Field ◽  
Many Body ◽  
Chiral Effective Field Theory ◽  
Hartree Fock ◽  
The Many ◽  
Three Body

Abstract.We study the effects of the nucleon-nucleon-lambda (NN$ \Lambda$Λ three-body force on neutron stars. In particular, we consider the NN$ \Lambda$Λ force recently derived by the Jülich-Bonn-Munich group within the framework of chiral effective field theory at next-to-next-to-leading order. This force, together with realistic nucleon-nucleon, nucleon-nucleon-nucleon and nucleon-hyperon interactions, is used to calculate the equation of state and the structure of neutron stars within the many-body non-relativistic Brueckner-Hartree-Fock approach. Our results show that the inclusion of the NN$ \Lambda$Λ force leads to an equation of state stiff enough such that the resulting neutron star maximum mass is compatible with the largest currently measured ( $ \sim 2 M_\odot$∼2M⊙ neutron star masses. Using a perturbative many-body approach we calculate also the separation energy of the $ \Lambda$Λ in some hypernuclei finding that the agreement with the experimental data improves for the heavier ones when the effect of the NN$ \Lambda$Λ force is taken into account.

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