基于Skyrme能量密度泛函的核物质宏观-微观质量公式研究
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"核物质的宏观-微观质量公式研究"
本研究基于标准的Skyrme能量密度泛函和扩展的Thomas-Fermi方法，对称和不对称核物质的特性以两个宏观“微观质量”公式表示：鲁布林“斯特拉斯堡核滴能量（LSD）”公式和Weizsäcker – Skyrme（WS *）公式是通过匹配有限核的每个粒子的能量来提取的。
首先，研究人员获得的对称核物质的不可压缩系数分别为Kˆž = 230±11 MeV和235±11 MeV。这些结果与Lattimer和Lim的液滴分析兼容。此外，对于LSD，对称能量在饱和密度下的斜率参数为L = 41.6±7.6 MeV，对于WS *，分别为51.5±9.6 MeV。
此外，本研究还研究了平均场等量标量和等矢量有效质量，以及中子物质的中子-质子有效质量分裂的密度依赖性。结果通常与Skyrme Hartree-Fock Bogoliubov计算和核子光势一致，标准偏差很大，并且随着密度的增加而迅速增加。有效质量的更好约束条件有助于减少平均场势深度的不确定性。
本研究的结果表明，基于标准的Skyrme能量密度泛函和扩展的Thomas-Fermi方法，可以很好地描述核物质的宏观-微观质量公式。这种方法可以提供一个有用的工具来研究核物质的性质，并且可以为未来核物理研究提供一个重要的参考。
本研究的贡献在于：
1. 提出了基于标准的Skyrme能量密度泛函和扩展的Thomas-Fermi方法来描述核物质的宏观-微观质量公式。
2. 获得了对称核物质的不可压缩系数分别为Kˆž = 230±11 MeV和235±11 MeV。
3. 研究了平均场等量标量和等矢量有效质量，以及中子物质的中子-质子有效质量分裂的密度依赖性。
4. 结果通常与Skyrme Hartree-Fock Bogoliubov计算和核子光势一致，标准偏差很大，并且随着密度的增加而迅速增加。
5. 有效质量的更好约束条件有助于减少平均场势深度的不确定性。
本研究为核物理研究提供了一个重要的参考，表明基于标准的Skyrme能量密度泛函和扩展的Thomas-Fermi方法可以很好地描述核物质的宏观-微观质量公式，并且可以为未来核物理研究提供一个有用的工具。
Physics Letters B 751 (2015) 553–558
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Properties of nuclear matter from macroscopic–microscopic mass
formulas
Ning Wang
a,b,∗
, Min Liu
a
, Li Ou
a
, Yingxun Zhang
c
a
Department of Physics, Guangxi Normal University, Guilin 541004, China
b
State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
c
China Institute of Atomic Energy, Beijing 102413, China
a r t i c l e i n f o a b s t r a c t
Article history:
Received
7 July 2015
Received
in revised form 4 November 2015
Accepted
4 November 2015
Available
online 10 November 2015
Editor:
W. Haxton
Based on the standard Skyrme energy density functionals together with the extended Thomas–Fermi
approach, the properties of symmetric and asymmetric nuclear matter represented in two macroscopic–
microscopic
mass formulas: Lublin–Strasbourg nuclear drop energy (LSD) formula and Weizsäcker–
Skyrme
(WS*) formula, are extracted through matching the energy per particle of finite nuclei. For LSD
and WS*, the obtained incompressibility coefficients of symmetric nuclear matter are K
∞
= 230 ±11 MeV
and
235 ± 11 MeV, respectively. The slope parameter of symmetry energy at saturation density is
L = 41.6 ±7.6MeVfor LSD and 51.5 ±9.6MeVfor WS*, respectively, which is compatible with the liquid-
drop
analysis of Lattimer and Lim [4]. The density dependence of the mean-field isoscalar and isovector
effective mass, and the neutron–proton effective masses splitting for neutron matter are simultaneously
investigated. The results are generally consistent with those from the Skyrme Hartree–Fock–Bogoliubov
calculations and nucleon optical potentials, and the standard deviations are large and increase rapidly
with density. A better constraint for the effective mass is helpful to reduce uncertainties of the depth of
the mean-field potential.
© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
Equation of state (EOS) for cold nuclear matter [1,2], e.g.,
the energy per particle of nuclear matter e(ρ, δ) = e(ρ, 0) +
E
sym
(ρ)δ
2
+ O(δ
4
) considered as a function of the nuclear den-
sity
ρ and the isospin asymmetry δ = (ρ
n
− ρ
p
)/(ρ
n
+ ρ
p
) where
ρ
n
and ρ
p
denote neutron and proton densities, respectively, plays
a key role in the interpretation of nuclear structure and nucleus–
nucleus
collisions, and as well as of neutron stars and supernova
explosions. Its knowledge is therefore highly desirable. In addition
to the properties of symmetric nuclear matter, especially the be-
havior
of its density dependence [3–12], has also attracted a lot
attention in recent years. The information of the symmetry energy
at saturation and sub-saturation densities is obtained from nuclear
dynamical behavior in heavy-ion collisions at intermediate and low
energies [13–15], and the static properties of finite nuclei such
as neutron skin thickness [16–19] and nuclear masses [20–27].
Although a great effort has been devoted in recent decades to
*
Corresponding author.
E-mail
address: wangning@gxnu.edu.cn (N. Wang).
investigate the properties of nuclear matter, the uncertainty of nu-
clear
symmetry energy E
sym
(ρ) is still large, for example, the slope
parameter L of the symmetry energy at the saturation density
extracted from some independent analyses of various experimen-
tal
observations is distributed in a range of 20 < L < 120 MeV
[28].
Therefore, more investigations with high precision are still
required.
As
one of the basic quantities in nuclear physics, the nuclear
masses can provide important information on the EOS at sub-
saturation
and saturation densities. For example, the energy per
particle of symmetric nuclear matter and symmetry energy at sat-
uration
density can be estimated by the coefficient of volume term
and symmetry energy coefficient in the liquid drop formula, re-
spectively.
Some nuclear mass models such as the Skyrme Hartree–
Fock–Bogoliubov
(HFB) models [22,23] and the macroscopic–
microscopic
mass models [20,21,29], have been successfully es-
tablished
with an rms error of 300–600 keV with respect to more
than 2000 measured nuclear masses. As macroscopic–microscopic
mass formulas, both the Lublin–Strasbourg–Drop (LSD) formula
[29] and the Weizsäcker–Skyrme (WS*) formula [20,21] use the
Strutinsky’s shell correction method for the microscopic part and
similar liquid drop formula for the macroscopic energy of a spher-
http://dx.doi.org/10.1016/j.physletb.2015.11.006
0370-2693/
© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.
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