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
Texas A&M University-Commerce
F. Fattoyev, J. Hooker, W. Newton and Jun Xu, TAMU-Commerce
Andrew Steiner, INT, University of Washington
Che Ming Ko, Texas A&M University
Lie-Wen Chen, Xiao-Hua Li and Bao-Jun Chai, Shanghai Jiao Tong University
Chang Xu, Nanjing University
Xiao Han and Gao-Feng Wei, Xi’an Jiao Tong University
Symmetry Energy and Neutron-Proton Effective Mass Splitting in Neutron-Rich Nucleonic Matter
Isospin diffusion data:
M.B. Tsang et al., PRL. 92, 062701 (2004);
T.X. Liu et al., PRC 76, 034603 (2007)
Transport model calculations
B.A. Li and L.W. Chen, PRC72, 064611 (05)
A. Steiner and B.A. Li, PRC72, 041601 (05)
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)
Bao-An Li and Andrew W. Steiner, Phys. Lett. B642, 436 (2006)
APR: K0=269 MeV.
The same incompressibility for symmetric nuclear matter of K0=211 MeV for x=0, -1, and -2
Astronomers discover the fastest-spinning neutron-star
Science 311, 1901 (2006).
W.G. Newton, talk at NN2012
Chen, Ko and Li, PRL (2005)
Agrawal et al.
Community averages with physically meaningful error bars?
independent of the interaction and many-body theory,
telling us what determines the Esym(ρ0) and L?
of Esym(ρ0) and L?
1) For a 1-component system
at saturation density, P=0, then
2) For a 2-components system
at arbitrary density
The Lane potential
Higher order in isospin asymmetry
C. Xu, B.A. Li, L.W. Chen and C.M. Ko, NPA 865, 1 (2011)
Relationship between the symmetry energy and the mean-field potentials
Both U0 (ρ,k) and Usym(ρ,k) are density and momentum dependent
Isoscarlar effective mass
Using K-matrix theory, the conclusion is independent of the interaction
R. Chen et al., PRC 85, 024305 (2012).
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 distributions
Xiao-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
Applying the constraints from neutron-nucleus scattering
Prediction for CREX
At the mean-field level:
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
Single nucleon potential within the HF approach using a modified Gogny force:
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).
What is the Equation of State of neutron-rich nucleonic matter?
Energy per nucleon in symmetric matter
Energy per nucleon in asymmetric matter
The axis of new opportunities
Essentially , all models and interactions available have been used to predict the Esym (ρ)
Symmetry energy (MeV)
Effective field theory
(Kaiser et al.)
A.E. L. Dieperink et al., Phys. Rev. C68 (2003) 064307
Skyrme Hartree-Fock and Relativistic Mean-Field predictions
L.W. Chen, C.M. Ko and B.A. Li, Phys. Rev. C72, 064309 (2005); C76, 054316 (2007).
The physical importance of L
In 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?
Stable neutron star
Requiring simultaneous solutions in both gravity and strong interaction!
Grand Unified Solutions of Fundamental Problems in Nature!
Size of the pasta phase and symmetry energy
W.G. Newton, M. Gearheart and Bao-An Li
ThThe Astrophysical Journal (2012) in press.
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 critical proton fraction for direct URCA process to happen is Xp=0.14 for npeμ matter obtained from energy-momentum conservation on the proton Fermi surface
Slow cooling: modified URCA:
Consequence: long surface
thermal emission up to a few
Faster cooling by 4 to 5 orders of magnitude: direct URCA
kaon condensation allowed
Neutron bubbles formation
transition to Λ-matter
B.A. Li, Nucl. Phys. A708, 365 (2002).
Z.G. Xiao et al, Phys. Rev. Lett. 102 (2009) 062502
Bao-An Li, Phys. Rev. Lett. 88 (2002) 192701
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
TOV equation: a condition at hydrodynamical equilibrium
For npe matter
P. Danielewicz, R. Lacey and W.G. Lynch,
Science 298, 1592 (2002))
dP/dρ<0 if E’sym is big and negative (super-soft)
Simon DeDeo, Dimitrios Psaltis
Phys. Rev. Lett. 90 (2003) 141101
Dimitrios Psaltis, Living Reviews in Relativity, 11, 9 (2008)
Tolman-Oppenheimer-Volkoff (TOV) equation:
a condition for hydrodynamical equilibrium
Do we really know gravity at short distance?
Not at all!
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
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)
Yukawa 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
In terms of the gravitational potential
A low-field limit of several alternative gravity theories
Yasunori Fujii, Nature 234, 5-7 (1971); G.W. Gibbons and B.F. Whiting, Nature291, 636 - 638 (1981)
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).
Supersoft Symmetry Energy Encountering Non-Newtonian Gravity in Neutron Stars
De-Hua Wen, Bao-An Li and Lie-Wen Chen, PRL 103, 211102 (2009)
EOS including the Yukawa contribution
B.A. Li, L.W. Chen and C.M. Ko, Physics Reports 464, 113 (2008)
Probing the symmetry energy at supra-saturation densities
π-/ π+ probe of dense matter
n/p ratio at supra-normal densities
A super-soft nuclear symmetry energy is favored by the FOPI data!!!
Z.G. Xiao, B.A. Li, L.W. Chen, G.C. Yong and M. Zhang, Phys. Rev. Lett. 102 (2009) 062502
W. Reisdorf et al.
NPA781 (2007) 459
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 dominates
At 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
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
Ratio of neutrons in the two
Mechanism for enhanced n/p ratio of pre-equilibrium nucleons
The first PRL paper connecting the symmetry energy
with heavy-ion reactions