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Advantages of EOS Studies with 400 MeV/u FRIB Upgrade

Explore the major physics issues regarding the EOS of neutron-rich nucleonic matter and their astrophysical impacts. Discuss experimental observables and the competitiveness of FRIB upgrade in EOS studies.

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Advantages of EOS Studies with 400 MeV/u FRIB Upgrade

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  1. Advantages for Equation-of-State Studies New Science Opportunities with a 400 MeV/u FRIB Upgrade Bao-An Li Based on talks and discussions at the Workshop on the Equation of State, organized by W.G. Lynch and M.B. Tsang, Detroit, June 28, 2018 Participants: Bill Lynch, Ed Brown, Zbigniew Chajecki, Katerina Chatziioannou, Pawel Danielewicz, Umesh Garg, Jeremy Holt, Chuck Horowitz, Cheming Ko, Bao-An Li, Brian David Metzger, J. B. Natowitz, Jorge Piekarewicz, David Radice, Madappa Prakash, Sanjay Reddy, Luke Roberts, Ingo Tews, Betty Tsang and Sherry J. Yennello

  2. Outline • What are the major physics issues regarding the EOS of neutron-rich nucleonic matter? • What are their immediate astrophysical impacts? • How/what experimental observables should be measured to address the major issues? • What are the competitiveness of FRIB upgrade in EOS studies compared to similar facilities under construction?

  3. W.A. Zajc,arXiv:1707.01993: Closing Remarks at Quark Matter 2017 Probing properties of nuclear matter with heavy-ion collisions over the last 40 years

  4. The EOS of cold, neutron-rich nucleonic matter symmetry energy Isospin asymmetry δ 12 12 12 Energy per nucleon in symmetric matter 18 18 3 Energy in asymmetric nucleonic matter Symmetric matter ρn=ρp ? ?? density New opportunities Isospin asymmetry ????

  5. Goal-1: determine the symmetry energy between 1-2𝞺0 at FRIB upgrade N.B. Zhang and B.A. Li, arXiv:1807.07698

  6. Single-nucleon (Lane) potential in isospin-asymmetric matter Isovector According to the Hugenholtz-Van Hove (HVH) theorem: J. Dabrowski and P. Haensel, PLB 42, (1972) 163. S. Fritsch, N. Kaiser and W. Weise, NPA. A750, 259 (2005).C. Xu, B.A. Li, L.W. Chen, Phys. Rev. C 82 (2010) 054607. Potential Kinetic Nucleon effective mass in isospin symmetric matter Neutron-proton effective mass splitting in neutron-rich matter B.A. Li et al., Prog. in Part. and Nucl. Phys. 99 (2018) 29.

  7. Momentum dependence of the symmetry/isovector potential Isovector optical potential from nucleon-nucleus scattering & (p,n) charge exchange reactions J. W. Holt, N. Kaiser, G. A. Miller Phys. Rev. C 93, 064603 (2016)

  8. What are the fundamental physics behind the symmetry energy? • Isospin dependence of strong interactions and correlations • Neutron-proton effective mass splitting in n-rich matter M.A. Preston and R.K. Bhaduri, Structure of the Nucleus, 1975 In a simple interacting Fermi gas model: Isospin-dependent correlation function Isospin-dependent effective 2-body interaction Specific issues to be addressed with reactions at FRIB upgrade • Momentum dependence of the symmetry potential due to the finite-range of isovector int. • Short-range correlations due to the tensor force in the isosinglet n-p channel • Spin-isospin dependence of the 3-body force • Isovector interactions of △(1232) resonances and their spectroscopy (mass and width) • Possible sign inversion of the symmetry potential at high momenta

  9. Parameterizing the EOS of symmetric matter and symmetry energy for the NS core Naturally approach asymptotically their Taylor expansions near the saturation density Current status of the restricted cold EOS parameter space: The minimum model of neutron stars: The pressure in the npeμ matter:

  10. Constraints on L as of 2013 based on 29 analyses of data L≈ 2 Esym(ρ0)=59±16 MeV Bao-An Li and  Xiao Han, Phys. Lett. B727 (2013) 276 L=58.7±28.1 MeV Fiducial value as of 2016 from surveying 53 analyses M. Oertel, M. Hempel, T. Klähn, S. Typel Review of Modern Physics 89 (2017) 015007

  11. Gravity-EOS Degeneracy in massive neutron stars Strong-field gravity: what is the nature of gravity? ? gravity GR+[Modified Gravity] Action S=Sgravity+Smatter ======== Massive neutron stars Matter+[Dark Matter]+[Dark Energy] EOS ? Nature of dense neutron-rich matter: What are the composition and EOS of neutron star matter?

  12. Signatures of high-density Esym in GW signals: Tidal deformability and mergers Gravitational Waves = “Ripples in space-time” Shibata, Keisuke; PRD73, 064027 (2006) • Tidal field Eij drives f-mode (quadrupole deformation Qij) • Resulting energy transfer appears as phase shift in gravitational waveform • Phase shift depends on one parameter: tidal polarizability λ (or Love number k2) Qij = -λEij M,R M’ a Flanagan, Hinderer, PRD77, 021502 (2008) Hinderer et al, PRD81, 123016 (2010) The k2 depends on R and M (EOS) through a very complicated differential equation

  13. Radii Tidal polarizability 3D symmetry energy parameter space skewness curvature slope Most probable symmetry energy with L=60 MeV

  14. Among the promising observables of high-density symmetry energy: • π -/π + and n/p spectrum ratio, neutron-proton differential flow and correlation function in heavy-ion collisions at intermediate energies • Radii of neutron stars • Neutrino flux of supernova explosions • Tidal polarizability in neutron star mergers, strain amplitude of gravitational waves from deformed pulsars, frequency and damping time of neutron star oscillations • A major scientific motivation of • High-energy rare isotope beam facilities around the world • Neutron Star Interior Composition Explorer (NICER of NASA) and various x-ray satellite (Chandra, LOFT, XMM-Newton, etc) • (3) Various gravitational wave detectors EPJA, Vol. 50, No. 2 (2014)

  15. FRIBU energy increase (X2) and beam intensity increase (X8) Examples: 48Ca+64Ni; 132Sn+124Sn & 238U+238U Slide from Bill Lynch, Zbigniew Chajecki, Pawel Danielewicz & Betty Tsang

  16. Isospin fraction during heavy-ion reactions highdensity region is more neutron-rich withsoftsymmetry energy n/p spectrum ratio of pre-equilibrium emission probing neutron-proton effective mass splitting π -/π + ratio at freeze-out and neutron-proton differential flow probing high-density Esym Bao-An Li, Phys. Rev. Lett. 88 (2002) 192701

  17. Probing the symmetry energy at supra-saturation densities Symmetry energy Stiff Central density density π-/ π+ probe of dense matter Soft Esym Stiff Esym n/p ? n/p ratio at supra-saturation densities

  18. Near-threshold π-/π+ ratio as a probe of symmetry energy at supra-normal densities W. Reisdorf et al. for the FOPI collaboration , NPA781 (2007) 459 IQMD: Isospin-Dependent Molecular Dynamics C. Hartnack, Rajeev K. Puri, J. Aichelin, J. Konopka, S.A. Bass, H. Stoecker, W. Greiner Eur.Phys.J. A1 (1998) 151-169 Using effective interactions Need a symmetry energy softer than the above to make the pion production region more neutron-rich!

  19. Circumstantial Evidence for a Super-soft Symmetry Energy at Supra-saturation 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

  20. Probing high-density symmetry energy using charged pion spectrum ratio from SPiRIT TPC (RIKEN) Probing neutron-proton effective mass splitting using high-energy neutron/proton spectrum ratio (NSCL) M.B. Tsang et al., PRC. 95.044614 (2017). Y.X. Zhang, M.B. Tsang et al. Slide from Bill Lynch, Zbigniew Chajecki, Pawel Danielewicz & Betty Tsang

  21. Neutron-proton differential transverse flow as a probe of isospin-dependence of nuclear force, Bao-An Li, PRL 85, 4221 (2000). Canceling out the isoscalar force but adding up the opposite isovector forces for neutrons and protons

  22. QMD analysis of GSI data on neutron-proton relative elliptical flow Central Au+Au, 400 MeV/A, Dan Cozma, Euro Phys. J. A 54: 40 (2018). P. Russotto et al. (ASY-EOS Coll), Phys. Rev. C94, 034608 (2016).

  23. Current status: density dependence of symmetry energy ? Natowitz Betty Tsang et al., PRC 86, 105803 (2012). Chuck Horowitz et al., JPG: 41, 093001(2014) Bao-An Li, Nuclear Physics News 27, 7 (2017)

  24. Comparison of RIKEN capability to FIRB-upgrade Based on BUU transport model (Danielewicz’s code) predictions Maximum density increases by 10% from RIKEN (40% from NSCL) Pion cross-section increases by 10 FRIB Upgrade boost intensities, asymmetry and pion cross-sections Intensity increase: Allow explorations of more asymmetric systems. Energy increase: yields increase exponentially above pion thresholds Regions around r=2r0 become more extensive Slide from Bill Lynch, Zbigniew Chajecki, Pawel Danielewicz & Betty Tsang

  25. Momentum dependence of the symmetry/isovector potential R. Chen et al. PRC 85:024305 (2012) FRIB Upgrade amplifies effects of the isovector potential with higher asymmetries FRIB Upgrade enables probing the momentum dependence in a larger region, thus the neutron-proton effective mass splitting in dense matter FRIB Upgrade answers the question if the isovevtor potential changes its sign at high momenta

  26. Ongoing and planned experiments probing the density dependence of nuclear symmetry energy Slide from Bill Lynch, Zbigniew Chajecki, Pawel Danielewicz & Betty Tsang

  27. Summary (1) The single, most important quantity to be measured with heavy-ion reactions at FRIB Upgrade is the density and momentum dependence of the nucleon isovector potential Usym,1(k,𝞺), subsequently the neutron-proton effective mass splitting and the symmetry energy between 1-2𝞺0 determining the radii and tidal polarizability of neutron stars (2) Multi-messengers approach for EOS studies=Experiments + Observations + Theories X neutrons Einstein FRIB-upgrade

  28. EoS from NS and HIC A recent analysis of the neutron star merger event provided a constraint on the nuclear matter EoS pressure vs. density as well as the tidal deformability [1]. The pressure for symmetric matter has been obtained from Au+Au collisions [2]. This can be extended to asymmetric matter using heavy Ion collisions at 2r0 at the FRIB upgrade e.g. pion yield ratios in 132Sn+124Sn collisions at E/A=400 MeV. Neutron star merger and radii are sensitive to 2r0. Most energy at FRIB is below threshold for pion productions. FRIB-U allows us to explore this region with higher intensity and pion cross-sections. By coupling neutron star models with nuclear physics models [3], tighter constraints on deformability and radius can be obtained from heavy-ion collisions. [1] LIGO/VIRGO collaboration, arXiv:1805.11579 (2018) [2] Danielewicz, Lynch & Lacey, Science 298, 1592 (2002) [3] Tsang et. al., arXiv:1807.06571

  29. Isoscalar Excitation Modes of Nuclear Resonance Isoscalar Giant Resonances: Isospin dependence of incompressibility Nothing conclusive about Ksym G. Colò, U. Garg, H. Sagawa, Eur. Phys. J. A 50, 26 (2014)

  30. Kt= Ksym – 6L – Q0L/K∞ Kt = -550 ± 100 MeV • Uncertainty in Kτ can be reduced to 50 MeV. • 0.5 MeV difference in EGMR corresponds to 80 MeV difference in Kτ

  31. Systematics from over 520 Skyrme+RMF energy density functionals Ingo Tews, James M. Lattimer, Akira Ohnishi, Evgeni E. Kolomeitsev  Astrophysics J. 848, 105 (2017)

  32. Skewness J0 of symmetric matter 173 Skyrme+101 RMF predictions Indications of model analyses of data Cai et al. N.B. Zhang et al., Nucl. Sci. Tech., 28, 181 (2017) P. Danielewicz, R. Lacey, & W.G. Lynch, Science, 298, 1592 (2002) B.J. Cai & L.W. Chen, Nucl. Sci. Tech., 28, 185 (2017) A. W. Steiner, J.M. Lattimer & E. F. Brown, APJ, 722, 33 (2010). Current status of the restricted EOS parameter space:

  33. Effects of symmetry energy on the crust-core transition density Parameterized EOS for the core N.B. Zhang, B.A. Li and J. Xu, APJ 859, 90 (2018) NV+BPS EOS for the crust Lattimer & Prakash, Phys. Rep., 442, 109 (2007)

  34. Astrophysical constraints on the high-density EOS parameters in 3D Low-density parameters are fixed at their most probable values J0 High-density E0(𝞺) Controlling M Ksym High-density Esym(𝞺) Controlling R Jsym

  35. Constraining the radii ofneutron stars with terrestrial experiments Bao-An Li and Andrew W. Steiner, Phys. Lett. B642, 436 (2006) Radii of neutron stars inferred from observations • thermal emissions from quiescent neutron star low-mass X-ray binaries (qLMXBs) • photospheric radius expansion (PRE) bursts with H and/or He atmosphere models . Nuclear limits J.M. Lattimer and A.W. Steiner, European Physics Journal A50, 40 (2014) APR: K0=269 MeV. Review of techniques & controversies: M.C. Miller & F.K. Lamb, European Physics Journal A 52, 63 (2016). Fitting isospin diffision data from Betty Tsang et al L.W. Chen, C.M. Ko and B.A. Li, Phys. Rev. Lett 94, 32701 (2005)

  36. 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 RMF Example: proton fractions with interactions/models leading to negative symmetry energy VMB M. Kutschera et al., Acta Physica Polonica B37 (2006) with tensor force Tensor force and/or 3-body force can make Esym negative at high densities Affecting the threshold of hyperon formation, kaon condensation, etc 3-body force effects in Gogny or Skyrme HF Super-Soft

  37. An example of EOS-Gravity degeneracy Simon DeDeo, Dimitrios Psaltis Phys. Rev. Lett. 90 (2003) 141101 Dimitrios Psaltis, Living Reviews in Relativity, 11, 9 (2008) • Neutron stars are among the densest objects with the strongest gravity • General Relativity (GR) may break down at strong-field limit and there is no fundamental reason to choose Einstein’s GR over alternative gravity theories • Need at least 2 observables to break the degeneracy Uncertain range of EOS Stiff EOS: V. R. Pandharipande, Nucl. Phys. A 174, 641 (1971). Soft EOS: R. B. Wiringa, V. Fiks, and A. Fabrocini, Phys. Rev. C38, 1010 (1988) Scalar-Tensor theory with quadratic coupling:

  38. Signatures of symmetry energy in GW signals: Tidal deformability and mergers F. Fattoyev, J. Carvajal, W.G. Newton and B.A. Li, PRC87, 15806 (2013) Λ of light NS is sensitive to L Λ of canonical and more massive NS is sensitive to high-density Esym but not L • Detector sensitivities assuming optimally oriented, • equal mass binary at D=100 Mpc • Damour, Nagar, PRD81, 084016 (2010) • Hinderer et al, PRD 81, 123016 (2010) arXiv:1802.05510 Z.Y. Zhu et al. APJ (2018) in press.

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