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Symmetry Energy and Equations of Statesfor Nuclear Matter
Myung-Ki Cheoun
Soongsil University, Seoul, Korea
Heavy Ion Meeting (HIM), Korea University, May 24, 2013
Contents1. Symmetry energy in Equations of state (EoSs)
2. Symmetry Energy and Pairing Correlations
3. GMR and PDR(GDR) in Finite Nuclei and Symmetry Energy
4. Symmetry Energy and Eq. of States above saturation density for Nuclear Matter from Heavy Ion Scattering
5. EoSs for Compact Cosmological Objects
6. PV electron scattering, Neutrino scattering and Sym. Energy
7. An application of Sym. Energy and EoSs in N-Astrophysics
8. Summary HIM Meeting, Korea University, May 24, 2013
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Asymmetry
Sym. Energy is given by the difference of the SNM and PNM energy !!
Symmetry Energy Definition by Energy per nucleon
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Sym. Energy at sat. density
Sym. Pressure
Sym. (in)compressbility
Sym. Energy has still some ambiguities !!
More refined values may be obtained from the Low Energy Reactions ? !!
Symmetry Energy S. Energy, Pressure and Incompressbility
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Since N=Z nuclei show the
dependence of N and Z, the pairing
should be considered !!
To explain the superfluid
plausible in neutron rich nuclei,
one needs the transition to the
BCS phase owing to the
pairings of nucleons !!
Symmetry Energy Why Pairing Energy in Sym. Energy ?
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Pairing gap in symmetric matter
Pairing gap in neutron matter
Pairing Gaps by the CD Bonn potentials are
reproduced to some extent in our RMF model !!
The Urca process is in progress !! 2013-05-24
Symmetry Energy Pairing Energy in Nuclear Matter
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The larger K_A, which can be calculated by the
EWSR of the GMR, the stiffer is the nucleus !! 2013-05-24
GMR and PDR Iso-scalar GMR (Breathing Mode)
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Our results show, the heavier Sn, the softer is
the incompressbility !! Detailed micoroscopic
understanding is in progress !! 2013-05-24
GMR and PDR Iso-scalar GMR in Sn Isotopes
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PDR is the resonance between the neutron skin
and the symmetric core, in particular, neutron-
rich and neutron halo nuclei !! 2013-05-24
GMR and PDR Iso-vector GDR and PDR
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2013-05-24
GMR and PDR Results of GDR and PDR by QRPA
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PDR is increased with the heavier Sn isotopes !!
Detailed analysis for the K value are in progress !!
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GMR and PDR Results of GDR and PDR by QRPA
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Eq. of State Low Density from N. Reactions
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Z
N e
2
+
N e
N e
2
Z
N e
2
N e
Z
N e
eh
)scattering (elastic
Ne
LR
LRA
2
e e pp
652
F 1010factorsform4
G-
Q
How to Measure the Neutral weak form factors (matter radius) ???
Matter Distribution PV electron and Neutrino scatteringK. S. Kim and MKC, JSPJ 82(2013), 024201
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Data from FOPI HIC exp.
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But, NS may collapse by the super-soft EOS !!!There is a new analysis.One needs more experimental data !!!
Eq. of State Intermediate Density from HIC
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Symmetry energy is still uncertain at high densities !!And it strongly depends on given models.
Eq. of State High Density from Neutron Stars
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Eq. of State Results by RMFs in SU(3)
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SU(3) extension may lead to massive NS about
2.0 Solar Mass, even with hyperons !! ??
RMF + CQMC
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T. Miyatsu, MKC et.al, arXiv:1304-1871[astro-ph]
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Eq. of State Results by RMFs in SU(3)
In np phase
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For alpha = -1(+1), more steeper (softer)EOS and more massive (light) Masses !!
Eq. of State Results by the MTOV from modified Gravity
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Modified TOV
Hyperonic NS may go to 2.0 solar mass by the modified gravity with reasonable magnetic field without any modification in RMF !! 19
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In np and nph phase with stronger magnetic field
For stronger m. field, we obtain more stiffer EOS andmore massive Masses !! May compensate modifiedgravity (alpha >0).
Eq. of State Results by MTOV and Magnetic fields
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MKC et.al, arXiv:1304-1871[astro-ph]
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Eq. of State Results by DDRMF
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Gamma factors from experiments may be exploited in RMFand predict EoS and MR relations of Neutrons Stars !!
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Eq. of State Results by DDRMF with mag. field
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Mass-radius relation of neutron stars may dependheavily on the gamma factor in the Symmetry energy !!!
Gamma_i = 0.69
C-Y. Ryu and MKC, submitted for publication
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Application of EoS Pulsar Kick and Spin Decce. in N-Star
)( 0 BΔσΔσσσ
Nuclear Matter ⇒ RMF Approach
Different Mean-Field for p, n & Λ
Fermi Motion, Mom.Dep.-Spin Vector, EoS
Neutrino Reactions and Transport by Boltz
mann Eq.
Magnetic-Field is treated perturbatively
Full Relativistic
Magnetic Field increases neutr
inos emitted in the direction
parallel to the magnetic field
and decreases that in
its opposite direction
Asymmetry of neutrino emission in SN explosion
T. Maruyama, MKC et.al, PRD 86(2012), 123003; PRD 83 081303(2011)
HIM Meeting, Korea University, May 24, 2013
Summary and Conclusion
1. Symmetry energy and equations of state for nuclear
(finite and infinite) matter systems are one of the main
goals in RAON physics.
2. Pairing gaps leading to the BCS phase are to be
studied in detail for the symmetry energy research.
3. For finite nuclei, we tested our nuclear model (QRPA
and DQRPA) for GMR and PDR data and deduce the
information for the symmetry energy.
4. For the information in intermediate density, heavy ion
scattering could be vital for the EoS. For high density,
observational data of neutrons stars may constrain the
EoS. But many ambiguities still remained.
5. For a consistent model for finite and infinite matter, we
are developing the RMF with the nucleon structure, the
pairing, the density dependence and the deformation.
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Thanks for your Attention !!
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CollaboratorsEunja Ha, Y. S. Kwon, Kiseok Choi, T. Miyatsu, M. Kusakabe(Soongsil University)
C. Ryu (Hanyang Univ.), K. S. Kim (Korea Aviation Univ.)W. So (Kangwon Univ.), C. Hyun (Daegu Univ.)…
K. Tsushima (Adelaide Univ.), K. Saito (TSU)
G. Mathews (Notre Dam), Baha Ballantekin (Wisconsin), Alex Brown (MSU)
T. Kajino, Ko Nakamura (NAOJ and Tokyo Univ.)T. Maruyama (Nihon Univ.), T. Hayakawa, S. Chiba (JAEA)
C. Deliduman… (Turkey)A. Faessler, F. Simkovic (Tuebingen Univ.)…
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Backup Files
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Nuclear
Structure & Matter
Nuclear Theory
Medical &
Bio application
RI Material
Research
Precision Mass
Measurement & Laser
Spectroscopy
Main Research Subjects
- Direct measurements of proton and alpha capture reactions
- Search for Super Heavy Elements beyond Z=113
Nuclear
Astrophysics &
Nucleosynthesis
Nuclear Data
- RI nuclear structure of neutron rich nuclei near N=126, 80<A<140- Symmetry energies at sub-saturation density
- Neutron capture cross section measurements by using n-TOF
- Development of RI nuclear theories
- Development of new cancer therapy
- Biological effect of tissue and DNA by RI beam
- Search for new material and its properties with β-NMR/μSR and
RI beam
- Hyperfine structure and characteristics of element and nuclei
Nuclear
Science
Atomic &
Molecular
Science
Material
Science
Medical &
Bio
Science
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Symmetry Energy S. Energy, Pressure and Incompressbility
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Pairing gap
equation:
Where vpp(k,p) is pairing interaction matrix elements:
For nuclear matter, RHB equations are:
Where:
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Symmetry Energy Pairing Energy in Nuclear Matter
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GMR and PDR Iso-vector GDR and PDR
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GMR and PDR Results of GDR and PDR by QRPA
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Eq. of State High Density from Neutron Stars
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Motivation 2: Modified Gravity
2012 KPS Fall Meeting, Phoenix Park, Oct. 27
How will be the modified gravity effect in the stellar scale ???
Motivation 2-1 : Yukawa Potential + Newtonian Gravity
2012 KPS Fall Meeting, Phoenix Park, Oct. 27
Solution of the Einstein eq. for a given time independent and spherical symmetric metric
exp[ν(r)] = 1 − 2GM(r)/rc2With a boundaryconditions on a boundaryand continuous metric
Standard TOV
Theoretical Frameworks 1 : Standard TOV
2012 KPS Fall Meeting, Phoenix Park, Oct. 27
If 1/c2 terms go to 0,Newtonian Gravity
Modified E. Equation
Modified TOV
Theoretical Frameworks 2: Modified TOV by M. Gravity
2012 KPS Fall Meeting, Phoenix Park, Oct. 27
If alpha dep. terms go to 0,Standard Gravity
Modified Action
In nph phase
HIM Meeting, Korea University, May 24, 2013
For alpha = -1 and stronger m. field,more steeperEOS and more massive Masses !!
Hyperonic NS may go to 2.0 solar mass by the modified gravity with reasonable magnetic field without any modification in RMF !!
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