symmetry energy and neutron-proton effective mass splitting in neutron-rich nucleonic matter
DESCRIPTION
Bao-An Li Texas A&M University-Commerce Collaborators: F. Fattoyev, J. Hooker, W. Newton and Jun Xu, TAMU-Commerce Andrew Steiner, INT, University of Washington Che Ming Ko, Texas A&M University - PowerPoint PPT PresentationTRANSCRIPT
Bao-An Li Texas A&M University-Commerce
Collaborators:F. Fattoyev, J. Hooker, W. Newton and Jun Xu, TAMU-CommerceAndrew Steiner, INT, University of WashingtonChe Ming Ko, Texas A&M UniversityLie-Wen Chen, Xiao-Hua Li and Bao-Jun Chai, Shanghai Jiao Tong UniversityChang Xu, Nanjing UniversityXiao Han and Gao-Feng Wei, Xi’an Jiao Tong University
Symmetry Energy and Neutron-Proton Effective Mass Splitting
in Neutron-Rich Nucleonic Matter
Outline:1.Why am I here? Connection with the PREX-CREX experiments
2. Why is the symmetry energy is still so uncertain even at saturation density?
a) Decomposition of the symmetry energy Esym (ρ0) and its slope L according to the Hugenholtz-Van Hove (HVH) theorem
b) An attempt to find out the most uncertain components of L from global neutron-nucleus optical potentials
3. What can we say about the neutron-proton effective mass splitting if both the Esym (ρ0) and L are well determined by PREX-CREX experiments?
Constraints from both isospin diffusion and n-skin in 208Pb
ρ ρ
ρ
Neutron-skin from nuclear scattering: V.E. Starodubsky and N.M. Hintz, PRC 49, 2118 (1994);
B.C. Clark, L.J. Kerr and S. Hama, PRC 67, 054605 (2003)
Isospin diffusion data:M.B. Tsang et al., PRL. 92, 062701 (2004); T.X. Liu et al., PRC 76, 034603 (2007)
Hartree-Fock calculationsA. Steiner and B.A. Li, PRC72, 041601 (05)
PREX?
J.R. Stone
implication
Transport model calculationsB.A. Li and L.W. Chen, PRC72, 064611 (05)
112Sn+124Sn
Nuclear constraining the radii of neutron stars
APR: K0=269 MeV.The same incompressibility for symmetric nuclear matter of K0=211 MeV for x=0, -1, and -2
Bao-An Li and Andrew W. Steiner, Phys. Lett. B642, 436 (2006)
Nuclear limits
● .
Astronomers discover the fastest-spinning neutron-star
Science 311, 1901 (2006).
Chen, Ko and Li, PRL (2005)
Agrawal et al.PRL (2012)
Time Line
W.G. Newton, talk at NN2012
Upper limit
Lower limit
Thanks to the hard work of many of you
Community averages with physically meaningful error bars?
0 0( ) 31.6 MeV and L( ) 62.4 MeV
albeit without physically meaningful error barssymE
Why is the Esym(ρ) is still so uncertain even at saturation density?
• Is there a general principle at some level, independent of the interaction and many-body
theory, telling us what determines the Esym(ρ0) and L?
• If possible, how to constrain separately each component
of Esym(ρ0) and L?
Decomposition of the Esym and L according to the Hugenholtz-Van Hove (HVH) theorem
1) For a 1-component system
at saturation density, P=0, then
2) For a 2-components system at arbitrary density
Microphysics governing the E ( ) and L( ) according to the HVH theorem sym
C. Xu, B.A. Li, L.W. Chen and C.M. Ko, NPA 865, 1 (2011)
The Lane potentialHigher order in isospin asymmetry
Relationship between the symmetry energy and the mean-field potentials
Lane potential
Symmetry energy
Isoscarlar effective mass
kinetic isoscalar isovector
Using K-matrix theory, the conclusion is independent of the interaction
Both U0 (ρ,k) and Usym(ρ,k) are density and momentum dependent
Gogny HF
SHF
Usym,1 (ρ,p) in several models
R. Chen et al., PRC 85, 024305 (2012).
Usym,1 (ρ,p) in several models
Gogny
Usym,2 (ρ,p) in several models
GognyGogny
Usym,2 (ρ,p) in several models
Providing a boundary condition on Usym,1 (ρ,p) and Usym,2 (ρ,p) at saturation density from global neutron-nucleus scattering optical potentials using the latest and most complete data base for n+A elastic angular distributionsXiao-Hua Li et al., PLB (2103) in press, arXiv:1301.3256
Providing a boundary condition on Usym,1 (ρ,p) and Usym,2 (ρ,p) at saturation density from global neutron-nucleus scattering optical potentials using the latest data base for n+A elastic angular distributions
Xiao-Hua Li et al., PLB (2103) in press, arXiv:1301.3256
Constraints on Ln
from n+A elastic scatterings
Applying the constraints from neutron-nucleus scattering
Time Line
Prediction for CREX
CREX
2016
±2
* * 0 0 0*
00
0*
( ) 3 ( ) 12 ( )1( )
( ) 1 2[ ( ) 1]
symn p
F
mL Em m mmm Em
0 0What can we learn if both E ( ) and L( ) are well determined?sym
*
0( ) 0.7 0.05mm
At the mean-field level:
Constraining the n-p effective mass splitting
* *0For E ( )=31 MeV, if L 85 MeV then m msym n p
Symmetry energy and single nucleon potential MDI used in the IBUU04 transport model
12'
'0 0 0 0
, 3 , ' 3 '2 2 2 2
0
0
0
1 2 2,
( , , , , ) ( ) ( ) ( ) (1 ) 81
2 2( , ') ( , ')' '1 ( '
' , ( ) 121 , ( ) 96 ,
) / 1 ( ') /
2112 1 1
u l
l u
BU p A A B
C Cf r p f r pd p d pp p
B BA A
x x x x x
x K MeVx
p
xx
p
ρ
C.B. Das, S. Das Gupta, C. Gale and B.A. Li, PRC 67, 034611 (2003).
B.A. Li, C.B. Das, S. Das Gupta and C. Gale, PRC 69, 034614; NPA 735, 563 (2004).
softsoft
stiff
stiff
Single nucleon potential within the HF approach using a modified Single nucleon potential within the HF approach using a modified Gogny force:Gogny force:
Density ρ/ρ0
The x parameter is introduced to mimic various predictions on the symmetry energy by different microscopic nuclear many-body theories using different effective interactions.It is the coefficient of the 3-body force term
Default: Gogny force
Potential energy density
Usym,1 (ρ,p) and Usym,2 (ρ,p) in the MDI potential used in IBUU04 transport
model
What is the Equation of State of neutron-rich nucleonic matter?
18 18
12
12
12
3
0 )) (, (( ) sn ymp
nn
p pE E E
( , )n pE
symmetry energy
ρ=ρn+ρp0
1
density
Isospin asymmetry
Symmetric matter
ρ n=ρ p
Energy per nucleon in symmetric matter
Energy per nucleon in asymmetric matter
δIsospin asymmetry
???
2
pure neutron matter symmetric nuclear matter2
1( ) ( ) ( )2sym
EE E E
The axis of new opportunities
???
???
???
14 30Normal density of nuclear matter 2.7 10 g/cm
Examples
Sym
met
ry e
nerg
y (M
eV)
Density
Effective field theory
(Kaiser et al.) DBHFRMF BHF
Greens function
Variational many-body
A.E. L. Dieperink et al., Phys. Rev. C68 (2003) 064307
Essentially , all models and interactions available have been used to predict the Esym (ρ)
More examples: Skyrme Hartree-Fock and Relativistic Mean-Field predictions
23 RMFmodels
ρ
L.W. Chen, C.M. Ko and B.A. Li, Phys. Rev. C72, 064309 (2005); C76, 054316 (2007).
Density
Among interesting questions regarding nuclear symmetry energy:• Why is the density dependence of symmetry energy so uncertain especially at
high densities?
• What are the major underlying physics determining the symmetry energy?
• What is the symmetry free-energy at finite temperature?
• What is the EOS of low-density clustered matter? How does it depend on the isospin asymmetry of the system? Linearly or quadratically? Can we still define a symmetry energy for clustered matter? What are the effects of n-p pairing on low density EOS?
• How to constrain the symmetry energy at various densities using terrestrial nuclear experiments and/or astrophysics observations?
Current Situation:• Many experimental probes predicted• Major progress made in constraining the symmetry energy around and below ρ0
• Interesting features found about the EOS of low density n-rich clustered matter• Several sensitive astrophysical observables identified/used to constrain Esym• High-density behavior of symmetry energy remains contraversial
Characterization of symmetry energy near normal density
The physical importance of LIn npe matter in the simplest model of neutron stars at ϐ-equilibrium
In pure neutron matter at saturation density of nuclear matter
Many other astrophysical observables, e.g., radii, core-crust transition density, cooling rate, oscillation frequencies and damping rate, etc of neutron stars
Neutron stars as a natural testing ground of grand unification theories of fundamental forces?
Nuclear force
weakE&M
Stable neutron star @ ϐ-equilibrium
Requiring simultaneous solutions in both gravity and strong interaction!Grand Unified Solutions of Fundamental Problems in Nature!
Connecting Quarks with the Cosmos: Eleven Science Questions for the New Century, Committee on the Physics of the Universe, National Research Council
• What is the dark matter? • What is the nature of the dark energy? • How did the universe begin? • What is gravity? • What are the masses of the neutrinos, and how have they shaped the evolution of the universe? • How do cosmic accelerators work and what are they accelerating? • Are protons unstable? • Are there new states of matter at exceedingly high density and temperature? • Are there additional spacetime dimensions? • How were the elements from iron to uranium made? • Is a new theory of matter and light needed at the highest energies?
Size of the pasta phase and symmetry energy
W.G. Newton, M. Gearheart and Bao-An LiThThe Astrophysical Journal (2012) in press.
Pasta
Torsional crust oscillations
M. Gearheart, W.G. Newton, J. Hooker and Bao-An Li, Monthly Notices of the Royal Astronomical Society, 418, 2343 (2011).
The proton fraction x at ß-equilibrium in proto-neutron stars is determined by
3 30 0(0.048[ / ( )] ( / )() 1 2 )symsymE Ex x
The critical proton fraction for direct URCA process to happen is XThe critical proton fraction for direct URCA process to happen is Xpp=0.14 for npe=0.14 for npeμμ matter obtained from energy-momentum conservation on the proton Fermi surfacematter obtained from energy-momentum conservation on the proton Fermi surface
Slow cooling: modified URCA:Slow cooling: modified URCA:( , ) ( , )
( , ) ( , )e
e
n n p p n p e
p n p n n p e
Faster cooling by 4 to 5 orders of Faster cooling by 4 to 5 orders of magnitude: direct URCAmagnitude: direct URCA
e
e
n p e
p n e
Consequence: long surface Consequence: long surface thermal emission up to a few thermal emission up to a few million yearsmillion years
B.A. Li, Nucl. Phys. A708, 365 (2002).
Direct URCA kaon condensation allowed
Neutron bubbles formationtransition to Λ-matter
Isospinseparationinstability
E(ρ,δ)= E(ρ,0)+Esym(ρ)δ2
Bao-An Li, Phys. Rev. Lett. 88 (2002) 192701
Z.G. Xiao et al, Phys. Rev. Lett. 102 (2009) 062502
TOV equation: a condition at hydrodynamical equilibrium
Gravity
Nuclear pressure
A challenge: how can neutron stars be stable with a super-soft symmetry energy?
If the symmetry energy is too soft, then a mechanical instability will occur when dP/dρ is negative, neutron stars will then all collapse while
they do exist in nature
For npe matter
dP/dρ<0 if E’sym is big and negative (super-soft)P. Danielewicz, R. Lacey and W.G. Lynch, Science 298, 1592 (2002))
A degeneracy: matter content (EOS) and gravity
in determining properties of neutron starsSimon DeDeo, Dimitrios Psaltis Phys. Rev. Lett. 90 (2003) 141101
• Neutron stars are among the densest objects with the strongest gravity
• General Relativity (GR) may break down at strong-field limit
• There is no fundamental reason to choose Einstein’s GR over alternative gravity theories
Uncertain range of EOS
Gravity
Nuclear pressure
In GR, Tolman-Oppenheimer-Volkoff (TOV) equation: a condition for hydrodynamical equilibrium
Dimitrios Psaltis, Living Reviews in Relativity, 11, 9 (2008)
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??????
In grand unification theories, conventional gravity has to be modified due to either geometrical effects of extra space-time dimensions at short length, a new boson or the 5th force
String theorists have published TONS of papers on the extra space-time dimensions
In terms of the gravitational potentialYukawa potential due to the exchange of a new boson proposed in the super-symmetric extension of the Standard Model of the Grand Unification Theory, or the fifth force
N. Arkani-Hamed et al., Phys Lett. B 429, 263–272 (1998); J.C. Long et al., Nature 421, 922 (2003); C.D. Hoyle, Nature 421, 899 (2003)
Yasunori Fujii, Nature 234, 5-7 (1971); G.W. Gibbons and B.F. Whiting, Nature 291, 636 - 638 (1981)
Do we really know gravity at short distance? Not at all!
The neutral spin-1 gauge boson U is a candidate, it is light and weakly interacting,Pierre Fayet, PLB675, 267 (2009), C. Boehm, D. Hooper, J. Silk, M. Casse and J. Paul, PRL, 92, 101301 (2004).
A low-field limit of several alternative gravity theories
Lower limit to support neutrons stars with a super-soft
symmetry energy
Upper limits
22 / g
EOS including the Yukawa contribution
Supersoft Symmetry Energy Encountering Non-Newtonian Gravity in Neutron StarsDe-Hua Wen, Bao-An Li and Lie-Wen Chen, PRL 103, 211102 (2009)
Promising Probes of the Esym(ρ) in Nuclear Reactions
At sub-saturation densities
Global nucleon optical potentials from n/p-nucleus and (p,n) reactions
Thickness of n-skin in 208Pb measured using various approaches and sizes of n-skins of unstable nuclei from total reaction cross sections
n/p ratio of FAST, pre-equilibrium nucleons Isospin fractionation and isoscaling in nuclear multifragmentation Isospin diffusion/transport Neutron-proton differential flow Neutron-proton correlation functions at low relative momenta t/3He ratio and their differential flow
Towards supra-saturation densities π -/π + ratio, K+/K0 ? Neutron-proton differential transverse flow n/p ratio of squeezed-out nucleons perpendicular to the reaction plane Nucleon elliptical flow at high transverse momentum t-3He differential and difference transverse flow
(1)Correlations of multi-observable are important(2) Detecting neutrons simultaneously with charged particles is critical
B.A. Li, L.W. Chen and C.M. Ko, Physics Reports 464, 113 (2008)
Probing the symmetry energy at supra-saturation densities
SoftSoft
Stiff
Stiff
Soft E sym
Stiff Esym
density
Symmetry energy
n/p ratio at supra-normal densities
Central density
π-/ π+ probe of dense matter
2( , ) ( ,0) ( )symE E E
n/p ?
Circumstantial Evidence for a Super-soft Symmetry Energy at Supra-saturation Densities
Z.G. Xiao, B.A. Li, L.W. Chen, G.C. Yong and M. Zhang, Phys. Rev. Lett. 102 (2009) 062502
A super-soft nuclear symmetry energy is favored by the FOPI data!!!
W. Reisdorf et al. NPA781 (2007) 459 Data:
Calculations: IQMD and IBUU04
Can the symmetry energy become negative at high densities?Yes, it happens when the tensor force due to rho exchange in the T=0 channel dominatesAt high densities, the energy of pure neutron matter can be lower than symmetric matter leading to negative symmetry energy
Example: proton fractions with interactions/models leading to negative symmetry energy
3 30 0(0.048[ / ( )] ( / )() 1 2 )symsymE Ex x
Soft
Super-Soft
M. Kutschera et al., Acta Physica Polonica B37 (2006)
Lunch conversation with Prof. Dr. Dieter Hilscher on a sunny day in 1993 at HMI in Berlin
neutrons
protons
Ratio of neutrons in the tworeaction systems
The first PRL paper connecting the symmetry energywith heavy-ion reactions
Mechanism for enhanced n/p ratio of pre-equilibrium nucleons