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Title: Variational theory of hot nucleon matter

Abstract

We develop a variational theory of hot nuclear matter in neutron stars and supernovae. It can also be used to study charged, hot nuclear matter which may be produced in heavy-ion collisions. This theory is a generalization of the variational theory of cold nuclear and neutron star matter based on realistic models of nuclear forces and pair correlation operators. The present approach uses microcanonical ensembles and the variational principle obeyed by the free energy. In this paper we show that the correlated states of the microcanonical ensemble at a given temperature T and density {rho} can be orthonormalized preserving their diagonal matrix elements of the Hamiltonian. This allows for the minimization of the free energy without corrections from the nonorthogonality of the correlated basis states, similar to that of the ground state energy. Samples of the microcanonical ensemble can be used to study the response, and the neutrino luminosities and opacities of hot matter. We present methods to orthonormalize the correlated states that contribute to the response of hot matter.

Authors:
;  [1]
  1. Department of Physics, University of Illinois at Urbana-Champaign, 1110 W. Green Street, Urbana, Illinois 61801 (United States)
Publication Date:
OSTI Identifier:
20995169
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevC.75.035802; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; FREE ENERGY; GROUND STATES; HAMILTONIANS; HEAVY ION REACTIONS; LUMINOSITY; MATRIX ELEMENTS; NEUTRINOS; NEUTRON STARS; NUCLEAR FORCES; NUCLEAR MATTER; NUCLEONS; OPACITY; STATISTICAL MODELS; VARIATIONAL METHODS

Citation Formats

Mukherjee, Abhishek, and Pandharipande, V. R. Variational theory of hot nucleon matter. United States: N. p., 2007. Web. doi:10.1103/PHYSREVC.75.035802.
Mukherjee, Abhishek, & Pandharipande, V. R. Variational theory of hot nucleon matter. United States. doi:10.1103/PHYSREVC.75.035802.
Mukherjee, Abhishek, and Pandharipande, V. R. Thu . "Variational theory of hot nucleon matter". United States. doi:10.1103/PHYSREVC.75.035802.
@article{osti_20995169,
title = {Variational theory of hot nucleon matter},
author = {Mukherjee, Abhishek and Pandharipande, V. R.},
abstractNote = {We develop a variational theory of hot nuclear matter in neutron stars and supernovae. It can also be used to study charged, hot nuclear matter which may be produced in heavy-ion collisions. This theory is a generalization of the variational theory of cold nuclear and neutron star matter based on realistic models of nuclear forces and pair correlation operators. The present approach uses microcanonical ensembles and the variational principle obeyed by the free energy. In this paper we show that the correlated states of the microcanonical ensemble at a given temperature T and density {rho} can be orthonormalized preserving their diagonal matrix elements of the Hamiltonian. This allows for the minimization of the free energy without corrections from the nonorthogonality of the correlated basis states, similar to that of the ground state energy. Samples of the microcanonical ensemble can be used to study the response, and the neutrino luminosities and opacities of hot matter. We present methods to orthonormalize the correlated states that contribute to the response of hot matter.},
doi = {10.1103/PHYSREVC.75.035802},
journal = {Physical Review. C, Nuclear Physics},
number = 3,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
  • We apply the variational theory for fermions at finite temperature and high density, developed in an earlier paper, to symmetric nuclear matter and pure neutron matter. This extension generalizes to finite temperatures, the many body technique used in the construction of the zero temperature Akmal-Pandharipande-Ravenhall equation of state. We discuss how the formalism can be used for practical calculations of hot dense matter. Neutral pion condensation along with the associated isovector spin longitudinal sum rule is analyzed. The equation of state is calculated for temperatures less than 30 MeV and densities less than three times the saturation density of nuclearmore » matter. The behavior of the nucleon effective mass in medium is also discussed.« less
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  • A variational wave function is constructed for a system of fermions interacting with a spin dependent potential. The correlations due to the repulsive core of the potential are described by a spin independent Jastrow product ansatz and the correlations due to the longer range part of the potential, which are assumed to be spin dependent, are described by an independent pair ansatz. A cluster expansion is derived for the variational energy and a set of hypernetted chain (HNC) equations obtained to sum the cluster series in terms of the elementary diagrams. Neglecting the elementary diagrams, the HNC equations are solvedmore » numerically for the spin dependent potential, V3, in neutron matter. The introduction of spin dependent correlations is found to give a small lowering of the variational energy in the HNC approximation. The results are very sensitive to an accurate treatment of the many-body terms within HNC approximation, however, and it is shown that additional approximations can easily lead to an exaggeration of the spin dependent correlations.« less
  • The reaction rates for electron capture, neutrino absorption, and neutrino scattering in hot asymmetric nuclear matter are calculated with two-body effective interactions and one-body effective weak operators obtained from realistic models of nuclear forces by use of correlated basis theory. The infinite system is modeled in a box with periodic boundary conditions, and the one-quasiparticle quasi-hole response functions are calculated with a large microcanonical sample and the Tamm-Dancoff approximation. Results for matter at a temperature of 10 MeV, proton fraction 0.4, and densities {rho}=(1/2),1,(3/2){rho}{sub 0}, where {rho}{sub 0} is the equilibrium density of symmetric nuclear matter, are presented to illustratemore » the method. In general, the strength of the response is shifted to higher-energy transfers when compared with that of a noninteracting Fermi gas. The shift in the response and the weakness of effective operators as compared with the bare operators significantly reduce the cross sections for electron capture and neutrino scattering by factors of {approx}2.5-3.5. In contrast, the symmetry energy enhances the neutrino absorption reaction rate relative to the Fermi gas. However, this reaction rate is still quite small because of Pauli blocking.« less