Study of the Nuclear Symmetry Energy: Study of the Nuclear Symmetry - PowerPoint PPT Presentation

Study of the Nuclear Symmetry Energy: Study of the Nuclear Symmetry Energy: Future theoretical directions Future theoretical directions Hermann Wolter University of Munich (LMU), Germany

Quest for the density dependence of Nuclear Symmetry Energy (NSE) - now for more than 20 years of intensive research, - still not well known, esp. at higher density - but important for very asymmetric nuclear systems (exotic nuclei), and in astrophysics Logo: ) ( MeV) Asy-stiff Β ) ( ) ( ) ( ρ Β Β Β ρ (ρ ρ E sym ( ( ( Asy-soft 0 1 2 3 ρ Β /ρ 0 Why? Since cannot be reliably calculated, one needs to look for observables in nuclear physics and astrophysics, strong interdependence of theory and experiment, -- experiments and observations: future prospects bright (see talks of E. Brown, G. Verde, Y. Leifels and Bill Lynch). -- theory: more expansion desirable, esp. in Europe

challenges in theory: - microscopic calculation: effective forces and many-body theory - theoretical interpretation of experiments a) nuclear structure beyond mean field b) HIC: transport approach c) astropysics: structure of NS and dynamics of CCSN Note 1: the NSE is a rather simple, stationary concept (a piece of the nuclear EoS) the way to study it involve much more complex systems (finite, dynamical, non-equilibrium) Note 2: all the above also true for the EOS in general, i.e. for symmetric nuclear matter. However, the NSE is a subdominant component of the EoS, and thus more difficult to observe and more difficult to calculate. We are now in the quantative era of the study of the NSE! This talk: try to identify the challenges in the theoretical treatments of the NSE and the possible future directions: illustrative and incomplete, qualitative, highly personal, but not supposed to be a summary. Evolved during workshop but special distracting event

Symmetry energy reviewed extensively in the past Science 23 April 2004: Vol. 304. no. 5670, pp. 536 - 542 DOI: 10.1126/science.1090720 Review The Physics of Neutron Stars J. M. Lattimer* and M. Prakash* Neutron stars are some of the densest manifestations of massive objects in the universe. They are ideal astrophysical laboratories for testing theories of dense matter physics and provide connections among nuclear physics, particle physics, and astrophysics. Neutron stars may exhibit conditions and phenomena not observed elsewhere, such as hyperon-dominated matter, deconfined quark matter, superfluidity and superconductivity with critical temperatures near 1010 kelvin, opaqueness to neutrinos, and magnetic fields in excess of 1013 Gauss. Here, we describe the formation, structure, internal composition, and evolution of neutron stars. Observations that include studies of pulsars in binary systems, thermal emission from isolated neutron stars, glitches from pulsars, and quasi- periodic oscillations from accreting neutron stars provide information about neutron star masses, radii, temperatures, ages, and internal compositions. Department of Physics and Astronomy, State University of New York, Stony Brook, NY 11794–3800, USA. …. difficult to say something new

What do we want to know about the NSE? ρ ρ − ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ δ δ δ δ = ρ ρ ρ ρ + ρ ρ ρ ρ δ δ δ δ + δ δ δ δ + δ δ δ δ = n p 2 4 E ( , ) / A E ( ) E ( ) O ( ) ... ρ ρ ρ ρ + ρ ρ ρ ρ B nm B sym B n p ∂ ∂ ∂ ∂ 2 2 ways to define: ρ ρ ρ ρ = = = = ρ ρ ρ ρ δ δ δ δ E ( ) 1 E ( , ) ∂ ∂ δ δ sym ∂ ∂ δ δ 2 2 δ δ δ δ = = = = 0 ρ ρ ρ ρ = = = = ρ ρ ρ ρ δ δ δ δ = = = = − − − − ρ ρ ρ ρ δ δ δ δ = = = = E sym ( ) E ( , 1 ) E ( , 0 ) � higher orders in δ δ δ δ not necessarily the same: � � � � � � � change of composition, with (solid) and without (dashed) e.g. clusterization stronger in SNM clusters physics independent of definitions. but dependent on how this SE is used: Astro (y), HIC (no) Need further information about the NSE, because of non-static systems ρ ρ ρ ρ δ δ δ δ = = = = ρ ρ ρ ρ + + + + ρ ρ ρ ρ τδ τδ τδ τδ + + + + U ( , k ; ) U ( , k ) U ( , k ) ( ) ... � 0 � � � � � � sym � � � � � � ρ ρ ρ ρ U ( , k ) τ τ τ τ − 1 ∂   m * m U = + τ τ τ τ τ τ τ τ   1 ∂  2  � m k k − − − − σ σ σ σ ρ ρ ρ ρ ( in med ) ( k ; ) NN Connected in a microscopic theory, or in a energy density functional. Also: Composition of asymmetric matter: important for astrophysical applications

Special representations of the SE: ρ ρ δ δ = ρ ρ + ρ ρ δ δ + δ δ + ρ ρ δ δ ρ ρ ρ ρ δ δ δ δ 2 4 E ( , ) / A E ( ) E ( ) O ( ) ... B nm B sym B expansion around ρ ρ 0 ρ ρ 2                 ρ ρ ρ ρ − − − − ρ ρ ρ ρ ρ ρ ρ ρ − − − − ρ ρ ρ ρ K L 0 0 0                 ρ ρ ρ ρ = = = = + + + + + + + + sym 0 0 E ( ) S                 ρ ρ ρ ρ sym ρ ρ ρ ρ 3         18         0 0 split into kin. and ⇒ ε ε ε ε ρ ρ ρ ρ ρ ρ ρ ρ + ρ ρ ρ ρ 2 / 3 pot 1 ( / ) E ( ) pot. symm energy 3 F 0 sym sym = ρ ρ ρ ρ ρ ρ ρ ρ γ γ γ γ pot E C ( / ) polynomial behavior implies 0 continuity between low and high densities: not necessarily so kinetic energy in a theoy with correlations not Fermi Gas a question of mapping microscopic theories to phenomenological approaches Σ Σ Σ Σ ρ ρ ρ ρ ⇔ ⇔ ⇔ ⇔ ρ ρ ρ ρ ( k , ) { m *, U ( )} Carbone, et al., EPJA50;13

The Nuclear Symmetry Energy in „realistic“ models Rel, Brueckner The EOS of symmetric and pure Nonrel. Brueckner neutron matter in different many- Variational Rel. Mean field body approaches Chiral perturb. C. Fuchs, H.H. Wolter, EPJA 30(2006)5,(WCI book) ����� SE The symmetry energy as the difference between symmetric and neutron matter: ���� = − E E E sym neutr . matt nucl . matt SE ist also momentum dependent � � effective mass � � asy-stiff Different proton/neutron effective masses m* n < m* p − ∂ 1 *   m U m = + q q  1  ∂ 2  �  m k k Isovector (Lane) asy-soft potential: momentum m* n > m* p data dependence = β − U ( k ) 1 ( U U ) β β β Lane neutr prot 2

More work has been done since then: Review by Marcello Baldo Horowitz, et al., JPhysG, 2014 Low density symmetry energy behave similarly and are consistent with analyses from nuclear structure and HIC. However, at high densities large differences. -- 3-body forces? (Baldo); scaling with density? -- short range tensor force (cut-off r c ) and in-medium mass scaling (parameter η η ) (B.A.Li) η η further work requred! Note: attempts to derive directly from QCD (QM-BB, QCD sum rules, holographic QCD, Skyrmions)

Symmetry energy at very low density (< 0.1 ρ ρ 0 ρ ρ 0 ) determined by cluster correlations 0 0 (Typel, et al., PRC81,015803(2010)) RMF model with explicit cluster degrees of freedon with thermal Green function approach to calculate medium modifications of clusters: NSE at ρ ρ � ρ ρ � 0 finite, because cluster low density symmetric matter gains energy by cluster formation � � Mott density: clusters melt, homogeneous p,n matter; here heavier nuclei Symmetry (embedded into a Energy gas) become important finite at T=0 due to cluster correlations

Investigation of very low density NSE in Heavy ion collisions e.g. experiment 64Zn+(92Mo,197Au) at 35 AMeV S. Kowalski, J. Natowitz, et al.,PRC75 014601 (2007) J. Natowitz, G. Röpke, S. Typel, .. PRL 104, 202501 (2010) symmetry energy „trajectory“ time, cooling cluster binding energies „differential“ freeze-out analysis: source reconstruction, analysis in terms of v surf ~time of emission determination of thermodyn. properties as fct of v surf determination of symmetry energy Assumptions need to be checked in transport calculations.