Transcript NN2012 Tensor force induced short-range correlation and high density behavior of nuclear symmetry energy Chang Xu (许 昌) Department of Physics, Nanjing Univerisity Collaborators: Bao-An Li.

NN2012
Tensor force induced short-range correlation and
high density behavior of nuclear symmetry energy
Chang Xu (许 昌)
Department of Physics, Nanjing Univerisity
Collaborators:
Bao-An Li (Texas A&M Univeristy-Commerce)
Zhongzhou Ren (Nanjing Univeristy)
Liewen Chen (Shanghai Jiaotong Univerity)
Outline
1. Brief introduction to symmetry energy
2. Theoretical framework and results
Esym and L at saturation density
Esym at supra-saturation densities
3. Short summary
1. Introduction
The density dependence of nuclear symmetry energy
------ a key issue in both nuclear physics and astrophysics
symmetry energy
Isospin asymmetry
1

2
 n   p 
1

E (  n ,  p )  E0 (  n   p )  Esym (  ) 






2
  
1
2
1
Energy1per3nucleon
in symmetric
nuclear8 matter8
Energy per nucleon in asymmetric nuclear matter
Recent progress on the symmetry energy:
1
Sub-saturation densities: some constraints have been
obtained from analyzing nuclear reaction data…
2 Saturation density: around 30 MeV from analyzing
nuclear masses and other data.
3 Supra-saturation densities : the situation is much less
clear because of very limited data available.
2. Theoretical Formulism
• Starting from the Hugenholtz–Van Hove theorem (HVH) that
is a fundamental relation among the Fermi energy, the
average energy per particle E and the pressure of the system P
at the absolute temperature of zero.
The nucleon single-particle potentials can be expanded as a
power series
isoscalar isovector
Lane potential:
Theoretical Formulism
Comparing the coefficient of each term then gives the
symmetry energy of any order
Xu et. al, Phys. Rev. C 82, 054607 (2010); Xu et. al, Nucl.Phys. A 865, 1 (2011)
BUU: The Momentum
dependent Interaction
(MDI)
The slope parameter L
which is important for determining several critical quantities, such as
the size of the neutron skin in heavy nuclei
location of the neutron drip line
core-crust transition density and gravitational binding energy of
neutron stars
……
Symmetry energy and its slope at saturation density
Systematics based on world data accumulated since 1969:
(1) Single particle energy levels from pick-up and stripping reaction
(2) Neutron and proton scattering on the same target at about the same energy
(3) Proton scattering on isotopes of the same element
(4) (p,n) charge exchange reactions
Constraining the symmetry energy near saturation density
using global nucleon optical potentials
C. Xu, B.A. Li and L.W. Chen, PRC 82, 054606 (2010).
Constraints extracted from data using various models
Iso. Diff & double n/p (ImQMD, 2009),
GOP: global optical potentials (Lane potentials)
C. Xu, B.A. Li and L.W. Chen, PRC 82, 054606 (2010) M. B. Tsang et al., PRL92, 122701 (2009).
Iso Diff. (IBUU04, 2005),
L.W. Chen et al., PRL94, 32701 (2005)
IAS+LDM (2009),
Danielewicz and J. Lee, NPA818, 36 (2009)
PDR (2010) of 68Ni and 132Sn,
A. Carbone et al., PRC81, 041301 (2010).
PDR (2007) in 208Pb
Land/GSI, PRC76, 051603 (2007)
SHF+N-skin of Sn isotopes,
L.W. Chen et al., PRC 82, 024301 (2010)
Isoscaling (2007),
D.Shetty et al. PRC76, 024606 (2007)
DM+N-Skin (2009): M. Centelles et al., PRL102, 122502 (2009)
TF+Nucl. Mass (1996), Myers and Swiatecki, NPA601, 141 (1996)
Symmetry energy at supra-saturation densities
• Some indications of a supersoft Esym at high densities have
been obtained from analyzing the π+/π− ratio data.
• Experiments have now been planned to investigate the highdensity behavior of the Esym at the CSR in China, GSI in
Germany, MSU in the United States, and RIKEN in Japan.
• Possible physical origins of the very uncertain Esym at suprasaturation densities?
U0 
U sym
Un  U p
3
1
uT 1  uT 0
2
4
4
Un  U p 1
1

 uT 1  uT 0
2
4
4

U0: relatively well determined
Usym is very poorly known especially at high momenta.
Effect of the spinisospin dependent
three-body force
Effects of the
short range tensor
force and nucleon
correlation
Xu et. al, Phys. Rev. C 81, 064612 (2010)
Effect of the spin-isospin dependent three-body force
The symmetry energy obtained with different spin dependence x0
and density dependence α in the three-body force (Gogny force)
Effect of the in-medium short-range tensor force
The pion and rho
meson exchanges
tensor forces
We use the BrownRho Scaling (BRS)
for the in-medium
rho meson mass
The tensor force leads to appreciable depletion/population of
nucleons below/above the Fermi surface in the single nucleon
momentum distribution in SNM.
Ekin(sym) is significantly below the Fermi gas model prediction
that is widely used in both nuclear physics and astrophysics
Microscopic calculations:
I. Vidana, A. Polls, C. Providencia, PRC 84, 062801 (2011).
A. Carbone, A. Polls, A. Rios, arXiv:1111.0797 (2011)
A. Lovato, private communications (2011)
The symmetry energy with different values of the BRS parameter
αBR= 0, 0.05, 0.10, 0.15, 0.20 using different values for the tensor
correlation parameter.
3. Summary
1.
General expressions are derived for Esym and L by using
the HVH theorem.
2.
Esym and L at normal density: extracted values from the
global optical potential
3.
The reason why the Esym and L at supra saturation
density so uncertain: isospin-dependence of the threebody force, tensor force and nucleon-nucleon correlation.
The three-body force and the tensor force induced SRC
will affects significantly the high-density behavior of
symmetry energy.
Thanks!
References
•
•
•
•
•
N. M. Hugenholtz and L. Van Hove, Physica 24, 363 (1958)
C. Xu, B. A. Li, L. W. Chen, and C. M. Ko, ArXiv:1004.4403.
K. A. Brueckner and J. Dabrowski, Phys. Rev. 134, B722 (1964).
J. Decharge and D. Gogny, Phys. Rev. C 21, 1568 (1980).
M. L. Ristig, W. J. Louw, and J. W. Clark, Phys. Rev.C 3, 1504
(1971).