Basic quantities of the equation of state in isospin asymmetric nuclear matter

• Published in: Nuclear science and techniques Vol. 32; no. 11; pp. 100 - 111
• Main Authors: Liu, Jie, Gao, Chao, Wan, Niu, Xu, Chang
• Format: Journal Article
• Language: English
• Published: Singapore Springer Singapore 01-11-2021; School of Physics,Nanjing University,Nanjing 210093,China%School of Physics and Optoelectronics,South China University of Technology,Guangzhou 510641,China
• Subjects: Beam Physics; Nuclear Energy; Particle Acceleration and Detection; Particle and Nuclear Physics; Physics; Physics and Astronomy; Symmetry energy; Single-nucleon potential; Equation of state; HVH theorem
• ISSN: 1001-8042; 2210-3147
• DOI: 10.1007/s41365-021-00955-2

Based on the Hugenholtz–Van Hove theorem, six basic quantities of the EoS in isospin asymmetric nuclear matter are expressed in terms of the nucleon kinetic energy
t
(
k
), the isospin symmetric and asymmetric parts of the single-nucleon potentials
U
0
(
ρ
,
k
)
and
U
sym
,
i
(
ρ
,
k
)
. The six basic quantities include the quadratic symmetry energy
E
sym,2
(
ρ
)
, the quartic symmetry energy
E
sym,4
(
ρ
)
, their corresponding density slopes
L
2
(
ρ
)
and
L
4
(
ρ
)
, and the incompressibility coefficients
K
2
(
ρ
)
and
K
4
(
ρ
)
. By using four types of well-known effective nucleon–nucleon interaction models, namely the BGBD, MDI, Skyrme, and Gogny forces, the density- and isospin-dependent properties of these basic quantities are systematically calculated and their values at the saturation density
ρ
0
are explicitly given. The contributions to these quantities from
t
(
k
),
U
0
(
ρ
,
k
)
, and
U
sym
,
i
(
ρ
,
k
)
are also analyzed at the normal nuclear density
ρ
0
. It is clearly shown that the first-order asymmetric term
U
sym,1
(
ρ
,
k
)
(also known as the symmetry potential in the Lane potential) plays a vital role in determining the density dependence of the quadratic symmetry energy
E
sym,2
(
ρ
)
. It is also shown that the contributions from the high-order asymmetric parts of the single-nucleon potentials (
U
sym
,
i
(
ρ
,
k
)
with
i
>
1
) cannot be neglected in the calculations of the other five basic quantities. Moreover, by analyzing the properties of asymmetric nuclear matter at the exact saturation density
ρ
sat
(
δ
)
, the corresponding quadratic incompressibility coefficient is found to have a simple empirical relation
K
sat,2
=
K
2
(
ρ
0
)
-
4.14
L
2
(
ρ
0
)
.