Bao-An Li. Collaborators: Bao-Jun Cai, Lie-Wen Chen, Chang Xu, Jun Xu, Zhi-Gang Xiao and Gao-Chan Yong

Transcription

1 Probing High-Density Symmetry Energy with Heavy-Ion Reactions Bao-An Li Collaborators: Bao-Jun Cai, Lie-Wen Chen, Chang Xu, Jun Xu, Zhi-Gang Xiao and Gao-Chan Yong

2 Outline What is symmetry energy? Why is it so uncertain especially at high densities? How to probe high-density symmetry energy with heavy-ion reactions?

3 EOS of cold, neutron-rich nucleonic matter E sym (ρ) = 1 2 E 2 δ E(ρ) E(ρ) 2 pure neutron matter symmetric nuclear matter 12 symmetry energy Isospin asymmetry δ 12 ρn ρ p E( ρn, ρ p) = E0 ( ρn = ρ p) + Es ym( ρ) + ο( δ 4 ) ρ 12 2 E( ρ, ρ ) n p Energy per nucleon in symmetric matter Energy in asymmetric nucleonic matter density

4 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 astrophysical observables, e.g., radii, core-crust transition density, cooling rate, oscillation frequencies and damping rate of isolated neutron stars as well as gravitational waves from deformed pulsars and/or neutron star binaries are sensitive to the density dependence of nuclear symmetry energy.

5 Constraints on E sym (ρ 0 ) and L based on 29 analyses of data Fiducial values as of Aug E sym (ρ 0 ) 31.6±2.66 MeV L 2 E sym (ρ 0 )=59±16 MeV L=2 E sym (ρ 0 ) if E sym =E sym (ρ 0 )(ρ/ρ 0 ) 2/3 Bao-An Li and Xiao Han, Phys. Lett. B727, 276 (2013).

6 Constraints on E sym (ρ 0 ) and L based on 53 analyses of data Fiducial values as of Oct. 12, 2016 Assuming! (1) Gaussian Distribution of L (2) Democratic principle (i.e., trust everyone) L 2 E sym (ρ 0 ) M. Oertel, M. Hempel, T. Klähn, S. Typel arxiv: [astro-ph.he]

7 What is the high-density symmetry energy? Predictions using energy density functionals and/or microscopic many-body theories The next talk by Wolfgang Trautmann??? Xiao et al Xiao et al M. B. Tsang et al., Phys. Rev. C86, (2012) P. Russotto et al. (ASY-EOS Collaboration), Phys. Rev. C94, (2016). Z.G. Xiao et al, Phys. Rev. Lett. 102, (2009).

8 Can the symmetry energy become negative at high densities? Yes, it happens when the tensor force due to ρ 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 Potential part of the 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 ( ρ ) / E ( ρ )] ( ρ / ρ )( 1 2 x ) sym sym Affecting the threshold of hyperon formation, kaon condensation, etc Both tensor force and/or 3-body force can make E sym negative at high densities 3-body force effects in Gogny or Skyrme HF

9 Neutron stars as a natural testing ground 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 Strong force weak What is the dark matter? What is the nature of the dark energy? How did the universe begin? What is gravity? Does Einstein s GR have a limit? Are there additional spacetime dimensions? 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? How were the elements from iron to uranium made? Is a new theory of matter and light needed at the highest energies?

10 Gravity-EOS Degeneracy in massive neutron stars Strong-field gravity: GR or Modified Gravity?? Massive neutron stars GR+[Modified Gravity] ======== Action S=S gravity +S matter Matter+[Dark Matter]+[Dark Energy]? Contents and stiffness of the EOS of super-dense matter? For high-density neutron-rich nucleonic matter, the most uncertain part of the EOS is the nuclear symmetry energy

11 Why is the symmetry energy so uncertain? (Besides the different many-body approaches used) Isospin-dependence of short-range neutron-proton correlation due to the tensor force Spin-isospin dependence of the 3-body force Isospin dependence of pairing and clustering at low densities (Valid only at the mean-field level) Keith A. Brueckner, Sidney A. Coon, and Janusz Dabrowski, Phys. Rev. 168, 1184 (1968) U n/ p (k,ρ,δ) =U 0 (k,ρ) ±U sym1 (k,ρ) δ +U sym2 (k,ρ) δ 2 +ο(δ 3 ) Within a simple interacting Fermi gas model Correlation functions V np (T0)? V np (T1) f T0? f T1, the tensor force in T0 channel makes them different

12 Dominance of the isosinglet (T=0) interaction At saturation density Paris potential Symmetry energy BHF Self-consistent Green s function I. Bombaci and U. Lombardo PRC 44, 1892 (1991) 2 1 E E sym ( ρ ) = E ( ρ ) 2 pure neutron matter E ( ρ ) 2 δ PRC68, (2003) symmetric nuclear matter

13 Uncertainty of the tensor force at short distance Takaharu Otsuka et al., PRL 95, (2005); PRL 97, (2006) Cut-off=0.7 fm for nuclear structure studies Gogny

14 What are Short Range Correlations (SRC) in nuclei? (Eli Piasetzky) 2N-SRC SRC ~R N LRC ~R A ~1 fm 1.f k F ~ 250 MeV/c High momentum tail: MeV/c 1.5 K F - 3 K F In momentum space: ρ o = 0.16 GeV/fm 3 1.7f 1.7f 1.8 fm Nucleons K 1 K 1 > K F, A pair with large relative momentum between the nucleons and small CM momentum. K 2 K 2 > K F

15 Tensor force induced (1) high-momentum tail in nucleon momentum distribution and (2) isospin dependence of SRC Theory of Nuclear matter H.A. Bethe Ann. Rev. Nucl. Part. Sci., 21, (1971) Fermi Sphere

16 Phenomenological nucleon momentum distribution n(k) including SRC effects guided by microscopic theories and experimental findings The n(k) is not directly measurable, but some of its features are observable. B.J. Cai and B.A. Li, PRC92, (R) (2015); PRC93, (2016). All parameters are fixed by (1) Jlab data: HMT in SNM=25%, 1.5% in PNM, (2) Contact C for SNM from deuteron wavefunction (3) Contact C in PNM from microscopic theories All parameters are assumed to have a linear dependence on isospin asymmetry as indicated by SCGF and BHF calculations

17 The high-momentum tail in deuteron scales as 1/K 4 O. Hen, L. B. Weinstein, E. Piasetzky, G. A. Miller, M. M. Sargsian and Y. Sagi, PRC92, (2015). VMB calculations VMB calculations Ultracold 6 Li and 40 K Ultracold 6 Li and 40 K =k/k F K =K/K F Stewart et al. PRL 104, (2010) Kuhnle et al. PRL 105, (2010)

18 E PNM ( ) (MeV) EOS and contact C of pure neutron matter Free Fermi Gas density (fm -3 ) The contact C of PNM is derived from its EOS Using Tan s adiabatic sweep theorem Eq. (6), = Tews, et al. Gezerlis, et al. Schwenk and Pethick Epelbaum, et al. Gezerlis, et al. B.J. Cai and B.A. Li, PRC92, (R) (2015). n(k)=c/k 4 S. Tan, Annals of Physics 323 (2008)

19 Modified Gogny Hartree-Fock energy density functional incorporating SRC-induced high momentum tail in the single nucleon momentum distribution Kinetic Two-body force Three-body force Momentum-dependent potential energy due to finite-range interaction SRC-induced HMT in the single-nucleon momentum distribution affects both the kinetic energy and the momentum-dependent part of the potential energy Bao-Jun Cai and Bao-An Li (2016)

20 Readjusting model parameters to reproduce the same saturation properties of nuclear matter as well as E sym (ρ 0 )=31.6 MeV and L(ρ 0) =58.9 MeV Consequence: Symmetry energy gets softened at both low and high densities The isospin-dependent part of the incompressibility at ρ 0 agrees better with data Data: MDI+HMT-exp: -492 MDI+FFG: -370

21 Probing the symmetry energy at high densities π - /π + in heavy-ion collisions Neutron-proton differential flow & n/p ratio in heavy-ion coll. Neutrino flux of supernova explosions Strength and frequency of gravitational waves Where does the E sym information get in, get out or get lost in pion production? *1 Isospin fractionation, i.e., the nn/pp ratio at high density is determined by the E sym (ρ) *2 The isovector potential for Delta resonance is completely unknown NN NΔ *5.Pion mean-field (dispersion relation), S and/or P wave and their isospin dependence are poorly known, existing studies are inconclusive. N+π How does the pion mean-field affect the Delta production threshold? Other final state interactions?

22 Formation of neutron-star matter in terrestrial nuclear laboratories Li Ou and Bao-An Li, Physical Review C84, (2011) Highly-magnetized, high-density, isospin-asymmetric matter formed in heavy-ion reactions * G

23 Isospin fractionation in heavy-ion reactions 2 E( ρ, δ ) = E( ρ,0) + E sym ( ρ) δ low (high) density region is more neutron-rich with stiff (soft) symmetry energy Bao-An Li, Phys. Rev. Lett. 88 (2002)

24 Pion ratio probe of symmetry energy at supra-normal densities nn a) Δ(1232) resonance model pp in first chance NN scatterings: np(pn) (negelect rescattering and reabsorption) 2 π N 2 = ( ) + 2 Z π 5N 5Z + + NZ NZ R. Stock, Phys. Rep. 135 (1986) 259. b) Thermal model: (G.F. Bertsch, Nature 283 (1980) 281; A. Bonasera and G.F. Bertsch, PLB195 (1987) 521) π exp[2( µ n µ p) / kt ] + π GC Coefficients 2 ρ m µ µ ( ) δ {ln ( ) ( )} n p n 3 m m m n p = Vasy Vasy VCoul + kt + bm T 2 n p p m m H.R. Jaqaman, A.Z. Mekjian and L. Zamick, PRC ( 1983) c) Transport models (more realistic approach): Bao-An Li, Phys. Rev. Lett. 88 (2002) , and several papers by others + π ρ ρ ρ λ 0 π π

25 Probing the symmetry energy at supra-saturation densities 2 E ( ρ, δ ) = E ( ρ, 0 ) + E sym ( ρ ) δ Symmetry energy Central density density π - /π + probe of dense matter Stiff E sym n/p? n/p ratio at supra-normal densities

26 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)

27 What is the high-density symmetry energy????

28 Summary The study on nuclear symmetry energy and its astrophysical impacts is Exciting! Symmetry energy at supra-saturation densities is the most uncertain part of the EOS of dense neutron-rich nucleonic matter Symmetry energy has significant effects on terrestrial experiments and astrophysical observables