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

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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

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

- Outline:
- 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?

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

ρρ

J.R. Stone

112Sn+124Sn

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)

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

.

●

Nuclear limits

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)

Upper limit

Agrawal et al.

PRL (2012)

Lower limit

Time Line

Community averages with physically meaningful error bars?

- 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?

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

Lane potential

Both U0 (ρ,k) and Usym(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

Gogny HF

SHF

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

Gogny

Gogny

Gogny

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

CREX

2016±2

Time Line

At the mean-field level:

crex

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

stiff

ρ

soft

Default: Gogny force

Density ρ/ρ0

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?

symmetry energy

Isospin asymmetry

δ

12

12

12

Energy per nucleon in symmetric matter

18

18

3

Energy per nucleon in asymmetric matter

Symmetric matter

ρn=ρp

density

???

0

ρ=ρn+ρp

???

The axis of new opportunities

???

1

Isospin asymmetry

???

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

Symmetry energy (MeV)

DBHF

Effective field theory

(Kaiser et al.)

RMF

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

ρ

Density

L.W. Chen, C.M. Ko and B.A. Li, Phys. Rev. C72, 064309 (2005); C76, 054316 (2007).

- 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

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
- • 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?

gravity

weak

E&M

Nuclear force

Stable neutron star

@

ϐ-equilibrium

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

Pasta

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:

E(ρ,δ)= E(ρ,0)+Esym(ρ)δ2

Consequence: long surface

thermal emission up to a few

million years

Isospin

separation

instability

Faster cooling by 4 to 5 orders of magnitude: direct URCA

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

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)

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
- There is no fundamental reason to choose
- Einstein’s GR over alternative gravity theories

??????

??

Nuclear pressure

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 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).

Upper limits

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

- Correlations of multi-observableare 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

Symmetry energy

Stiff

Central density

Soft

density

π-/ π+ probe of dense matter

Soft Esym

Stiff Esym

n/p ?

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

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 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)

Soft

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