Symmetry Energy and Neutron-Proton Effective Mass Splitting in Neutron-Rich Nucleonic Matter 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 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

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 E sym ( ρ 0 ) 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 E sym ( ρ 0 ) and L are well determined by PREX-CREX experiments?

Constraints from both isospin diffusion and n-skin in

208

Pb

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) ρ ρ J.R. Stone 112 Sn+ 124 Sn

implication

PREX?

Hartree-Fock calculations 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)

Nuclear constraining the radii of neutron stars

Bao-An Li and Andrew W. Steiner, Phys. Lett. B642, 436 (2006) ● .

APR: K 0 =269 MeV.

The same incompressibility for symmetric nuclear matter of K 0 =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) Upper limit Lower limit

Time Line

Agrawal et al.

PRL (2012)

Thanks to the hard work of many of you

Community averages with physically meaningful error bars?

E sym

(  0 )  31.6 MeV and L(  0 )  62.4 MeV albeit without physically meaningful error bars

Why is the E

sym

(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 E

sym

(ρ

0

) and L?

• If possible, how to constrain separately each component of E

sym

(ρ

0

) 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 sym 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

Lane potential Both U 0 ( ρ,k) and U sym ( ρ,k) are density and momentum dependent kinetic isoscalar isovector Symmetry energy Isoscarlar effective mass Using K-matrix theory, the conclusion is independent of the interaction

SHF Gogny HF

U

sym,1

(ρ,p) in several models

R. Chen et al., PRC 85, 024305 (2012).

U

sym,1

(ρ,p) in several models

Gogny

U

sym,

2

(ρ,p) in several models

Gogny Gogny

U

sym,

2

(ρ,p) in several models

Providing a boundary condition on U elastic angular distributions sym, 1 (ρ,p) and U sym, 2 (ρ,p) at saturation density from global neutron-nucleus scattering optical potentials using the latest and most complete data base for n+A Xiao-Hua Li et al., PLB (2103) in press, arXiv:1301.3256

Providing a boundary condition on U distributions sym, 1 (ρ,p) and U sym, 2 (ρ,p) at saturation density from global neutron-nucleus scattering optical potentials using the latest data base for n+A elastic angular Xiao-Hua Li et al., PLB (2103) in press, arXiv:1301.3256

Constraints on L

n from n+A elastic scatterings

Applying the constraints from neutron-nucleus scattering

Prediction for CREX

Time Line

CREX

What can we learn if both E

sym

(  0 ) and L(  0 ) are well determined?

At the mean-field level:

m

* (  0 ) 

m m

*

n



m

*

p

(  0 )   

m L

(  0

E sym

(  0

E F

(  0 )

m m

* (  0 )  1

m m

* (  0

Constraining the n-p effective mass splitting For E

sym

(

 0

)=31 MeV, if L



85 MeV then m

*

n



m

*

p

Symmetry energy and single nucleon potential MDI used in the IBUU04 transport model soft 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 Density ρ/ρ 0 Potential energy density

Single nucleon potential within the HF approach using a modified Gogny force:



U

( ,

p

,  ,

x

) 

A u

(

x

)    0 ' 

A l

(

x

)    0 

B

(  0 

x

 2 )  8 

x



B

 1     0  1   '  2

C

 0 

d

3

p

' 1  (

f



p



p

' ) ') 2 /  2  2

C

 0 ' 

d

3

p

' 1  (

f



p

' 

p

') ') 2 /  2 '   1 , 2

A l

(

x

)   121  2 

B x

 1 ,

A u

(

x

)   96  2 

B x

 1 ,

K

0  211

MeV

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).

U

sym,

1

(ρ,p) and U

sym,

2

(ρ,p) in the MDI potential used in IBUU04 transport model

   

E sym

 1  2

E

2   2 

E

 pure neutron matter 

E

 symmetric nuclear matter symmetry energy Isospin asymmetry δ 12

E

( 

n

, 

p

12 ) 

E

0 ( 

n

 

p

) 

E s ym

(  )   

n

 

p

   12   

E

(

n p

)  Energy per nucleon in symmetric matter 18 18 3 Energy per nucleon in asymmetric matter Normal density of nuclear matter  0  3 0 density ρ=ρ n + ρ p Isospin asymmetry

Essentially , all models and interactions available have been used to predict the E sym (ρ) Examples

BHF Greens function Variational many-body

Density

A.E. L. Dieperink et al., Phys. Rev. C68 (2003) 064307

More examples:

Skyrme Hartree-Fock and Relativistic Mean-Field predictions 23 RMF models Density L.W. Chen, C.M. Ko and B.A. Li, Phys. Rev. C72, 064309 (2005); C76, 054316 (2007).

•

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 ρ 0 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 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?

Connecting Quarks with the Cosmos: Eleven Science Questions for the New Century, Committee on the Physics of the Universe, National Research Council

E&M Nuclear force weak Stable neutron star @ ϐ-equilibrium • 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?

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 proton fraction x at ß -equilibrium in proto-neutron stars is determined by

x

 0.048[

E sym

(  ) /

E sym

(  0 3 )] ( 0 )( 1  3 The critical proton fraction for direct URCA process to happen is X p =0.14 for npe μ matter obtained from energy-momentum conservation on the proton Fermi surface Slow cooling: modified URCA:

n



p

   

e



e

Consequence: long surface thermal emission up to a few million years Faster cooling by 4 to 5 orders of magnitude: direct URCA

n p

 

p n

 

e e

     

e e

E( ρ,δ)= E(ρ,0)+E sym ( ρ)δ 2

Isospin separation instability Direct URCA kaon condensation allowed Neutron bubbles formation transition to Λ-matter

B.A. Li, Nucl. Phys.

A708

, 365 (2002).

Bao-An Li, Phys. Rev. Lett. 88 (2002) 192701

Z.G. Xiao et al, Phys. Rev. Lett. 102 (2009) 062502

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 Gravity Nuclear pressure 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)

A degeneracy: matter content (EOS) and gravity in determining properties of neutron stars

Simon DeDeo , Dimitrios Psaltis Phys. Rev. Lett. 90 (2003) 141101 Dimitrios Psaltis, Living Reviews in Relativity, 11, 9 (2008) Gravity • Neutron stars are among the densest objects with the strongest gravity ??????

• General Relativity (GR) may break down at strong-field limit ??

Nuclear pressure • There is no fundamental reason to choose Einstein’s GR over alternative gravity theories Uncertain range of EOS In GR, 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 5 th 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 In terms of the gravitational potential new boson proposed in the super-symmetric extension of the Standard Model of the Grand Unification Theory, or the fifth force A low-field limit of several alternative gravity theories Yasunori Fujii, Nature 234, 5-7 (1971); G.W. Gibbons and B.F. Whiting, Nature 291 , 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

g

2 /  2

Promising Probes of the E sym (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 208 Pb 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/ 3 He ratio and their differential flow Towards supra-saturation densities



π /π + ratio, K + /K 0 ?



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 3 He differential and difference transverse flow

(1) Correlations of m ulti-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

E

  

E

 

E sym

2 Symmetry energy Central density density π / π + probe of dense matter Stiff E sym

n/p ratio at supra-normal densities

n/p ?

Circumstantial Evidence for a Super-soft Symmetry Energy at Supra-saturation Densities Data:

W. Reisdorf et al. NPA781 (2007) 459

Calculations: IQMD and IBUU04

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

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)

x

 0.048[

E sym

(  ) /

E sym

(  0 0 )( 1 

x

3

Super -Soft

Lunch conversation with Prof. Dr. Dieter Hilscher on a sunny day in 1993 at HMI in Berlin Ratio of neutrons in the two reaction systems neutrons protons Mechanism for enhanced n/p ratio of pre-equilibrium nucleons The first PRL paper connecting the symmetry energy with heavy-ion reactions