150
Y. Leifels
12.1 Introduction
The nuclear matter equation of state (EOS) is one of central topics in nuclear physics.
It defines the evolution of nuclear reactions and the characteristics of compact stars
and cataclysmic astrophysical events like supernova explosions and neutron star
mergers. A theoretical determination of the nuclear EOS from first principles by
microscopic calculations using realistic two and three-body nuclear interactions
is highly non-trivial and a subject of current scientific research using different
approaches, i.e., quantum many-body theory in the Brueckner-Hartree-Fock approximation or chiral perturbation theory (ChPT). From astrophysical observations meaningful constraints can be obtained to the nuclear EOS, however, heavy-ion collisions
are the only means to study the characteristics of the nuclear EOS in the laboratory.
The nuclear EOS describes the relation between density, pressure, energy, temperature, and the isospin asymmetry δ = (ρ n − ρ p )/ρ, where ρ n , ρ p , and ρ are neutron,
proton, and nuclear matter densities, respectively. It is conventionally divided into a
symmetric matter part independent of the isospin asymmetry and an isospin term, also
quoted as symmetry energy E sym (ρ), that enters with a factor δ
2 into the equation of
state. In this description, the symmetry energy is the difference in the energy between
symmetric matter ρ n = ρ p and pure neutron matter. Different density dependencies
of E sym (ρ) can be described quantitatively by expanding the symmetry energy in
terms of (ρ − ρ 0 )/ρ 0 using the value of E sym,0 = E sym (ρ = ρ 0 ) and the slope parameter at normal nuclear matter density L = 3ρ 0
δ E sym (ρ)
δρ
| ρ=ρ 0 leading to the following
equation:
E sym (ρ) = E sym,0 +
L
3
(ρ − ρ 0 )
ρ 0
+
K sym
18
(ρ − ρ 0 )
ρ 0
2
+ ...,
where K sym is referred to as curvature parameter.
Microscopic calculations of the energy functional of nuclear matter employing
different approaches to the nucleon-nucleon interaction predict rather different forms
of the EOS. Most calculations for the symmetry energy coincide at or slightly below
normal nuclear matter density (compare Fig. 12.5 right panel), which demonstrates
that constraints from finite nuclei are active for an average density smaller than saturation density and surface effects play a role. In contrast to that extrapolations to
supra-normal densities diverge dramatically. The density dependence of the nuclear
symmetry energy is an important constituent for drip lines, masses, densities, and
collective excitations of neutron-rich nuclei [1], flows,m and multi-fragmentation in
heavy-ion collisions at intermediate energies [2, 3], but also for astrophysical phenomena like supernovae, neutron stars [4], and the merging of two neutron stars [5],
which have been recently observed and identified by the characteristic gravitational
wave signal and the simultaneous emission of γ -rays.
Many results of nuclear structure and nuclear reaction measurements as well
as astrophysical observations have been collected in [6]. The symmetry energy
E sym,0 and the slope parameter L at saturation density have been deduced to be
Y. Leifels
12.1 Introduction
The nuclear matter equation of state (EOS) is one of central topics in nuclear physics.
It defines the evolution of nuclear reactions and the characteristics of compact stars
and cataclysmic astrophysical events like supernova explosions and neutron star
mergers. A theoretical determination of the nuclear EOS from first principles by
microscopic calculations using realistic two and three-body nuclear interactions
is highly non-trivial and a subject of current scientific research using different
approaches, i.e., quantum many-body theory in the Brueckner-Hartree-Fock approximation or chiral perturbation theory (ChPT). From astrophysical observations meaningful constraints can be obtained to the nuclear EOS, however, heavy-ion collisions
are the only means to study the characteristics of the nuclear EOS in the laboratory.
The nuclear EOS describes the relation between density, pressure, energy, temperature, and the isospin asymmetry δ = (ρ n − ρ p )/ρ, where ρ n , ρ p , and ρ are neutron,
proton, and nuclear matter densities, respectively. It is conventionally divided into a
symmetric matter part independent of the isospin asymmetry and an isospin term, also
quoted as symmetry energy E sym (ρ), that enters with a factor δ
2 into the equation of
state. In this description, the symmetry energy is the difference in the energy between
symmetric matter ρ n = ρ p and pure neutron matter. Different density dependencies
of E sym (ρ) can be described quantitatively by expanding the symmetry energy in
terms of (ρ − ρ 0 )/ρ 0 using the value of E sym,0 = E sym (ρ = ρ 0 ) and the slope parameter at normal nuclear matter density L = 3ρ 0
δ E sym (ρ)
δρ
| ρ=ρ 0 leading to the following
equation:
E sym (ρ) = E sym,0 +
L
3
(ρ − ρ 0 )
ρ 0
+
K sym
18
(ρ − ρ 0 )
ρ 0
2
+ ...,
where K sym is referred to as curvature parameter.
Microscopic calculations of the energy functional of nuclear matter employing
different approaches to the nucleon-nucleon interaction predict rather different forms
of the EOS. Most calculations for the symmetry energy coincide at or slightly below
normal nuclear matter density (compare Fig. 12.5 right panel), which demonstrates
that constraints from finite nuclei are active for an average density smaller than saturation density and surface effects play a role. In contrast to that extrapolations to
supra-normal densities diverge dramatically. The density dependence of the nuclear
symmetry energy is an important constituent for drip lines, masses, densities, and
collective excitations of neutron-rich nuclei [1], flows,m and multi-fragmentation in
heavy-ion collisions at intermediate energies [2, 3], but also for astrophysical phenomena like supernovae, neutron stars [4], and the merging of two neutron stars [5],
which have been recently observed and identified by the characteristic gravitational
wave signal and the simultaneous emission of γ -rays.
Many results of nuclear structure and nuclear reaction measurements as well
as astrophysical observations have been collected in [6]. The symmetry energy
E sym,0 and the slope parameter L at saturation density have been deduced to be