Nuclear equation of state with the variational method and its application to supernova simulations

We report on an equation of state (EOS) of hot asymmetric nuclear matter constructed using the variational method and its application to hydrodynamic simulations of core-collapse supernovae. This nuclear EOS is based on the AV18 two-body potential and UIX three-body potential, and the energy per nucleon at zero temperature is constructed with the cluster variational method. At finite temperatures, the free energies per nucleon are calculated with an extension of the variational method devised by Schmidt and Pandharipande. This EOS is in good agreement with that by the Fermi hypernetted chain variational calculations at zero and finite temperatures, and the structure of neutron stars calculated with this EOS is consistent with recent observational data. Using this nuclear EOS, we perform a spherically symmetric general-relativistic adiabatic simulation of the SN explosion. The explosion energy calculated with our EOS in the present simulation is larger than that obtained with the Shen EOS, implying that the variational EOS is softer than the Shen EOS.

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VARIATIONAL CALCULATION FOR THE NUCLEAR EQUATION OF STATE TOWARD SUPERNOVA EXPLOSIONS

Modern Physics Letters A ◽

10.1142/s0217732308029575 ◽

2008 ◽

Vol 23 (27n30) ◽

pp. 2455-2458

Author(s):

MASATOSHI TAKANO ◽

HIROAKI KANZAWA ◽

KAZUHIRO OYAMATSU ◽

KOHSUKE SUMIYOSHI

Keyword(s):

Equation Of State ◽

Variational Method ◽

Symmetry Energy ◽

Nuclear Force ◽

Variational Calculation ◽

Expectation Value ◽

Nuclear Equation Of State ◽

Supernova Explosions ◽

Three Body ◽

Stability Line

The equation of state (EOS) is calculated for uniform nuclear matter at zero and finite temperatures with the variational method. Making use of uncertainty of the three-body nuclear force, adjustable parameters in the nuclear EOS are tuned so that the Thomas-Fermi calculations for β-stable nuclei with the EOS reproduce the empirical data. The calculated nuclear properties imply that larger symmetry energy of the EOS is preferable to reproduce the empirical β-stability line. The expectation value of the nuclear Hamiltonian caused by the 2π-exchange three-body nuclear force is uncertain and related to the symmetry energy.

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THE BETHE–BRUECKNER–GOLDTONE THEORY OF THE NUCLEAR EQUATION OF STATE AND NEUTRON STARS

International Journal of Modern Physics B ◽

10.1142/s0217979203020259 ◽

2003 ◽

Vol 17 (28) ◽

pp. 5127-5137 ◽

Cited By ~ 1

Author(s):

M. BALDO ◽

G. F. BURGIO

Keyword(s):

Equation Of State ◽

Neutron Stars ◽

Gluon Plasma ◽

Many Body ◽

Static Properties ◽

Many Body Theory ◽

Nuclear Equation Of State ◽

Pure Neutron Matter ◽

Particle Potential ◽

Three Body

The microscopic many-body theory of the Nuclear Equation of State is discussed in the framework of the Bethe–Brueckner–Goldstone method. The expansion is extended up to the three hole-line diagrams contribution. The Brueckner equation for the two-body G-matrix and the Bethe–Fadeev equation for the three-body scattering matrix are solved both for the gap and continuous choices of the single particle potential. For symmetric and pure neutron matter strong evidence of convergence in the expansion is found. Once three-body forces are introduced, the phenomenological saturation point is reproduced. In order to study neutron stars static properties, the theory is extended to include strangeness, and the possible quark-gluon plasma component is described in the simplified MIT bag model. The results for the mass and radius of neutron stars are briefly discussed.

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Variational Calculations for the Nuclear Equation of State toward Supernova Simulations

10.1063/1.2943583 ◽

2008 ◽

Author(s):

H. Kanzawa ◽

K. Oyamatsu ◽

K. Sumiyoshi ◽

M. Takano ◽

Takuma Suda ◽

...

Keyword(s):

Equation Of State ◽

Nuclear Equation Of State ◽

Variational Calculations

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CONSISTENT THREE-BODY FORCE WITH BONN B POTENTIAL AND NEUTRON STAR STRUCTURE

International Journal of Modern Physics E ◽

10.1142/s0218301310016156 ◽

2010 ◽

Vol 19 (08n09) ◽

pp. 1727-1733 ◽

Cited By ~ 1

Author(s):

Z. H. LI ◽

U. LOMBARDO ◽

H.-J. SCHULZE ◽

W. ZUO

Keyword(s):

Neutron Star ◽

Equation Of State ◽

Symmetry Energy ◽

Body Force ◽

Nucleon Force ◽

Nucleon Potential ◽

Saturation Properties ◽

Nuclear Equation Of State ◽

Neutron Star Mass ◽

Three Body

Microscopic three-nucleon force consistent with the Bonn B two-nucleon potential is constructed, which includes Δ(1232), Roper, and nucleon-antinucleon excitation contributions. Recent results for the choice of the meson parameters are discussed. The forces are used in Brueckner calculations and the saturation properties of nuclear matter are determined. At the high densities, the nuclear equation of state and the symmetry energy are calculated. The corresponding neutron star mass-radius relations are presented.

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