Cluster Correlations in Dilute Matter and Nuclei

Transcription

1 Cluster Correlations in Dilute Matter and Nuclei GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt Nuclear Astrophysics Virtual Institute Workhop on Weakly Bound Exotic Nuclei International Institute of Physics Federal University of Rio Grande do Norte Praiamar Hotel, Ponta Negra, Natal, Brazil May 24 30, 2015

2 Outline Motivation Astrophysics and Equation of State, Theoretical Approaches, Nuclear and Stellar Matter, Correlations, Objectives Generalized Relativistic Density Functional Details of grdf Model, Effective Interaction, Neutron Star Matter, Constraint from Heavy-Ion Collisions Symmetry Energy and Neutron Skins Density Dependence and Constraints, Application of grdf Model, Neutron Skins with α-cluster Correlations Conclusions and Outlook Cluster Correlations in Dilute Matter and Nuclei - 1

3 Motivation

4 Astrophysics and Equation of State essential ingredient in astrophysical model calculations: Equation(s) of State of dense matter dynamical evolution of supernovae static properties of neutron stars conditions for nucleosynthesis energetics, chemical composition, transport properties,... X-ray: NASA/CXC/J.Hester (ASU) Optical: NASA/ESA/J.Hester & A.Loll (ASU) Infrared: NASA/JPL-Caltech/R.Gehrz (Univ. Minn.) NASA/ESA/R.Sankrit & W.Blair (Johns Hopkins Univ.) Cluster Correlations in Dilute Matter and Nuclei - 2

5 Astrophysics and Equation of State essential ingredient in astrophysical model calculations: Equation(s) of State of dense matter dynamical evolution of supernovae static properties of neutron stars conditions for nucleosynthesis energetics, chemical composition, transport properties,... timescale of reactions timescale of system evolution equilibrium (thermal, chemical,... ) application of EoS reasonable X-ray: NASA/CXC/J.Hester (ASU) Optical: NASA/ESA/J.Hester & A.Loll (ASU) Infrared: NASA/JPL-Caltech/R.Gehrz (Univ. Minn.) NASA/ESA/R.Sankrit & W.Blair (Johns Hopkins Univ.) Cluster Correlations in Dilute Matter and Nuclei - 2

6 Astrophysics and Equation of State essential ingredient in astrophysical model calculations: Equation(s) of State of dense matter dynamical evolution of supernovae static properties of neutron stars conditions for nucleosynthesis energetics, chemical composition, transport properties,... timescale of reactions timescale of system evolution equilibrium (thermal, chemical,... ) application of EoS reasonable wide range of thermodynamic variables (temperature, density, isospin asymmetry) global EoS required simulation of core-collapse supernova Temperature, T [MeV] Baryon density, log (ρ [g/cm 3 ]) Baryon density, n B [fm 3 ] T. Fischer, Uniwersytet Wroc lawski Y e Cluster Correlations in Dilute Matter and Nuclei - 2

7 Theoretical Approaches to the EoS hadronic ab-initio methods with realistic interactions interactions: potential models, meson-exchange, chiral forces, RG evolved (Argonne, Urbana, Tucson-Melbourne, Nijmegen, Paris, Bonn,... ) two-body NN interaction (in vacuum) well constrained by experiment, three-body forces less, large uncertainties for YN, YY, etc. Cluster Correlations in Dilute Matter and Nuclei - 3

8 Theoretical Approaches to the EoS hadronic ab-initio methods with realistic interactions interactions: potential models, meson-exchange, chiral forces, RG evolved (Argonne, Urbana, Tucson-Melbourne, Nijmegen, Paris, Bonn,... ) two-body NN interaction (in vacuum) well constrained by experiment, three-body forces less, large uncertainties for YN, YY, etc. many-body methods: BHF/DBHF, SCGF, CBF, VMC, GFMC, AFDMC,... Cluster Correlations in Dilute Matter and Nuclei - 3

9 Theoretical Approaches to the EoS hadronic ab-initio methods with realistic interactions interactions: potential models, meson-exchange, chiral forces, RG evolved (Argonne, Urbana, Tucson-Melbourne, Nijmegen, Paris, Bonn,... ) two-body NN interaction (in vacuum) well constrained by experiment, three-body forces less, large uncertainties for YN, YY, etc. many-body methods: BHF/DBHF, SCGF, CBF, VMC, GFMC, AFDMC,... QCD-based/inspired descriptions Lattice QCD, DS, (P)NJL, bag models,... Cluster Correlations in Dilute Matter and Nuclei - 3

10 Theoretical Approaches to the EoS hadronic ab-initio methods with realistic interactions interactions: potential models, meson-exchange, chiral forces, RG evolved (Argonne, Urbana, Tucson-Melbourne, Nijmegen, Paris, Bonn,... ) two-body NN interaction (in vacuum) well constrained by experiment, three-body forces less, large uncertainties for YN, YY, etc. many-body methods: BHF/DBHF, SCGF, CBF, VMC, GFMC, AFDMC,... QCD-based/inspired descriptions Lattice QCD, DS, (P)NJL, bag models,... effective field theories (EFT) chiral EFT, nuclear lattice EFT Cluster Correlations in Dilute Matter and Nuclei - 3

11 Theoretical Approaches to the EoS hadronic ab-initio methods with realistic interactions interactions: potential models, meson-exchange, chiral forces, RG evolved (Argonne, Urbana, Tucson-Melbourne, Nijmegen, Paris, Bonn,... ) two-body NN interaction (in vacuum) well constrained by experiment, three-body forces less, large uncertainties for YN, YY, etc. many-body methods: BHF/DBHF, SCGF, CBF, VMC, GFMC, AFDMC,... QCD-based/inspired descriptions Lattice QCD, DS, (P)NJL, bag models,... effective field theories (EFT) chiral EFT, nuclear lattice EFT methods not always applicable (temperatures, asymmetries, densities) many EoS for neutron matter & neutron star matter, but no global EoS for astrophysical applications available from these approaches Cluster Correlations in Dilute Matter and Nuclei - 3

12 Theoretical Approaches to the EoS hadronic ab-initio methods with realistic interactions interactions: potential models, meson-exchange, chiral forces, RG evolved (Argonne, Urbana, Tucson-Melbourne, Nijmegen, Paris, Bonn,... ) two-body NN interaction (in vacuum) well constrained by experiment, three-body forces less, large uncertainties for YN, YY, etc. many-body methods: BHF/DBHF, SCGF, CBF, VMC, GFMC, AFDMC,... QCD-based/inspired descriptions Lattice QCD, DS, (P)NJL, bag models,... effective field theories (EFT) chiral EFT, nuclear lattice EFT methods not always applicable (temperatures, asymmetries, densities) many EoS for neutron matter & neutron star matter, but no global EoS for astrophysical applications available from these approaches only phenomenological models for global EoS at present Cluster Correlations in Dilute Matter and Nuclei - 3

13 Nuclear Matter & Stellar Matter nuclear matter only strongly interacting particles no electromagnetic interaction Cluster Correlations in Dilute Matter and Nuclei - 4

14 Nuclear Matter & Stellar Matter nuclear matter only strongly interacting particles no electromagnetic interaction below nuclear saturation density liquid-gas phase transition ( non-congruent ) coexistence of low/high-density phases with different isospin asymmetries precursor of clustering pressure p [kev fm -3 ] density n [fm -3 ] T = 10 MeV asymmetry β T = 10 MeV asymmetry β pressure p [MeV fm -3 ] 10 1 symmetric nuclear matter density n [fm -3 ] temperature T [MeV] symmetric nuclear matter chemical potential µ [MeV] Cluster Correlations in Dilute Matter and Nuclei - 4

15 Nuclear Matter & Stellar Matter nuclear matter only strongly interacting particles no electromagnetic interaction below nuclear saturation density liquid-gas phase transition ( non-congruent ) coexistence of low/high-density phases with different isospin asymmetries precursor of clustering stellar matter hadrons and leptons strong and electromagnetic interaction specific condition: charge neutrality formation of inhomogeneous matter new particle species, pasta phases quenching of liquid-gas phase transition lattice formation at low temperatures phase transition: liquid/gas solid pressure p [kev fm -3 ] density n [fm -3 ] T = 10 MeV asymmetry β T = 10 MeV asymmetry β pressure p [MeV fm -3 ] 10 1 symmetric nuclear matter density n [fm -3 ] temperature T [MeV] symmetric nuclear matter chemical potential µ [MeV] particle number density n i [fm -3 ] grdf, spherical Wigner-Seitz cell A heavy = Z heavy = 48.2 p n e 2 H 3 H 3 He 4 He T = 5 MeV n = 0.01 fm -3 Y p = radius r [fm] Cluster Correlations in Dilute Matter and Nuclei - 4

16 EoS for Astrophysical Applications constituents: mostly considered are nucleons, nuclei (light/heavy/representative), leptons, photons,... Cluster Correlations in Dilute Matter and Nuclei - 5

17 EoS for Astrophysical Applications constituents: mostly considered are nucleons, nuclei (light/heavy/representative), leptons, photons,... models: often combination of different approaches (Skyrme/Gogny/relativistic mean-field models, NSE, virial EoS, density functionals, classical/quantum molecular dynamics,... ) Cluster Correlations in Dilute Matter and Nuclei - 5

18 EoS for Astrophysical Applications constituents: mostly considered are nucleons, nuclei (light/heavy/representative), leptons, photons,... models: often combination of different approaches (Skyrme/Gogny/relativistic mean-field models, NSE, virial EoS, density functionals, classical/quantum molecular dynamics,... ) global EoS used in astrophysical simulations: H&W W. Hillebrandt, K. Nomoto, R.G. Wolff, A&A 133 (1984) 175 LS180/220/375 J.M. Lattimer, F.D. Swesty, NPA 535 (1991) 331 STOS (TM1) H. Shen, H. Toki, K. Oyamatsu, K. Sumiyoshi, NPA 637 (1998) 435, PTP 100 (1998) 1013 Cluster Correlations in Dilute Matter and Nuclei - 5

19 EoS for Astrophysical Applications constituents: mostly considered are nucleons, nuclei (light/heavy/representative), leptons, photons,... models: often combination of different approaches (Skyrme/Gogny/relativistic mean-field models, NSE, virial EoS, density functionals, classical/quantum molecular dynamics,... ) global EoS used in astrophysical simulations: H&W W. Hillebrandt, K. Nomoto, R.G. Wolff, A&A 133 (1984) 175 LS180/220/375 J.M. Lattimer, F.D. Swesty, NPA 535 (1991) 331 STOS (TM1) H. Shen, H. Toki, K. Oyamatsu, K. Sumiyoshi, NPA 637 (1998) 435, PTP 100 (1998) 1013 HS (TM1,TMA,FSUgold,NL3,DD2,IUFSU) M. Hempel, J. Schaffner-Bielich, NPA 837 (2010) 210 SHT (NL3) G. Shen, C.J. Horowitz, S. Teige, PRC 82 (2010) , , PRC 83 (2011) SHO (FSU1.7, FSU2.1) G. Shen, C.J. Horowitz, E. O Connor, PRC 83 (2011) SFHo/SFHx A.W. Steiner, M. Hempel, T. Fischer, ApJ 774 (2013) 17 recently many more, also with additional degrees of freedom (hyperons, quarks) Cluster Correlations in Dilute Matter and Nuclei - 5

20 Correlations information on correlations in spectral functions in general complicated structure Cluster Correlations in Dilute Matter and Nuclei - 6

21 Correlations information on correlations in spectral functions in general complicated structure approximation: quasiparticles with self-energies in-medium change of particle properties reduction of residual correlations Cluster Correlations in Dilute Matter and Nuclei - 6

22 Correlations information on correlations in spectral functions in general complicated structure approximation: quasiparticles with self-energies in-medium change of particle properties reduction of residual correlations quasiparticle concept very successful in nuclear physics phenomenological mean-field models (e.g. Skyrme, Gogny, relativistic) treatment of pairing correlations (Bogoliubov transformation) Cluster Correlations in Dilute Matter and Nuclei - 6

23 Correlations information on correlations in spectral functions in general complicated structure approximation: quasiparticles with self-energies in-medium change of particle properties reduction of residual correlations quasiparticle concept very successful in nuclear physics phenomenological mean-field models (e.g. Skyrme, Gogny, relativistic) treatment of pairing correlations (Bogoliubov transformation) matter at low densities: clusters/nuclei as new degrees of freedom benchmark: model independent virial equation of state Cluster Correlations in Dilute Matter and Nuclei - 6

24 Correlations information on correlations in spectral functions in general complicated structure approximation: quasiparticles with self-energies in-medium change of particle properties reduction of residual correlations quasiparticle concept very successful in nuclear physics phenomenological mean-field models (e.g. Skyrme, Gogny, relativistic) treatment of pairing correlations (Bogoliubov transformation) matter at low densities: clusters/nuclei as new degrees of freedom benchmark: model independent virial equation of state development of improved EoS model with correct limits and explicit cluster degrees of freedom Cluster Correlations in Dilute Matter and Nuclei - 6

25 Objectives development of improved EoS model with: Cluster Correlations in Dilute Matter and Nuclei - 7

26 Objectives development of improved EoS model with: extended set of constituent particles nuclear matter: nucleons, nuclei/clusters,..., mesons, hyperons,..., quarks stellar matter: add electrons, muons, photons Cluster Correlations in Dilute Matter and Nuclei - 7

27 Objectives development of improved EoS model with: extended set of constituent particles nuclear matter: nucleons, nuclei/clusters,..., mesons, hyperons,..., quarks stellar matter: add electrons, muons, photons more serious consideration of correlations nucleon-nucleon correlations: clustering, pairing Pauli principle: dissolution of composite particles in medium (Mott effect) electromagnetic correlations: essential for solidification/melting Cluster Correlations in Dilute Matter and Nuclei - 7

28 Objectives development of improved EoS model with: extended set of constituent particles nuclear matter: nucleons, nuclei/clusters,..., mesons, hyperons,..., quarks stellar matter: add electrons, muons, photons more serious consideration of correlations nucleon-nucleon correlations: clustering, pairing Pauli principle: dissolution of composite particles in medium (Mott effect) electromagnetic correlations: essential for solidification/melting better constrained model parameters constraints: properties of nuclei, compact stars, heavy-ion collisions Cluster Correlations in Dilute Matter and Nuclei - 7

29 Objectives development of improved EoS model with: extended set of constituent particles nuclear matter: nucleons, nuclei/clusters,..., mesons, hyperons,..., quarks stellar matter: add electrons, muons, photons more serious consideration of correlations nucleon-nucleon correlations: clustering, pairing Pauli principle: dissolution of composite particles in medium (Mott effect) electromagnetic correlations: essential for solidification/melting better constrained model parameters constraints: properties of nuclei, compact stars, heavy-ion collisions correct treatment of phase transitions distinguish nuclear matter and stellar matter non-congruent phase transitions, gas/liquid/solid(crystal) phases Cluster Correlations in Dilute Matter and Nuclei - 7

30 Objectives development of improved EoS model with: extended set of constituent particles nuclear matter: nucleons, nuclei/clusters,..., mesons, hyperons,..., quarks stellar matter: add electrons, muons, photons more serious consideration of correlations nucleon-nucleon correlations: clustering, pairing Pauli principle: dissolution of composite particles in medium (Mott effect) electromagnetic correlations: essential for solidification/melting better constrained model parameters constraints: properties of nuclei, compact stars, heavy-ion collisions correct treatment of phase transitions distinguish nuclear matter and stellar matter non-congruent phase transitions, gas/liquid/solid(crystal) phases challenge: covering of full range of thermodynamic variables in a unified model Cluster Correlations in Dilute Matter and Nuclei - 7

31 Generalized Relativistic Density Functional

32 Generalized Relativistic Density Functional extension of relativistic mean-field models with density-dependent meson-nucleon couplings Cluster Correlations in Dilute Matter and Nuclei - 8

33 Generalized Relativistic Density Functional extension of relativistic mean-field models with density-dependent meson-nucleon couplings selected model features: extended set of constituents: nucleons, light clusters ( 2 H, 3 H, 3 He, 4 He) and heavy nuclei experimental binding energies: AME 2012 (M. Wang et al., Chinese Phys. 36 (2012) 1603) extension: DZ10 predictions (J. Duflo, A.P. Zuker, Phys. Rev. C 52 (1995) R23) considered as quasi-particles with scalar and vector potentials proton number Z DZ AME neutron number N Cluster Correlations in Dilute Matter and Nuclei - 8

34 Generalized Relativistic Density Functional extension of relativistic mean-field models with density-dependent meson-nucleon couplings selected model features: extended set of constituents: nucleons, light clusters ( 2 H, 3 H, 3 He, 4 He) and heavy nuclei experimental binding energies: AME 2012 (M. Wang et al., Chinese Phys. 36 (2012) 1603) extension: DZ10 predictions (J. Duflo, A.P. Zuker, Phys. Rev. C 52 (1995) R23) considered as quasi-particles with scalar and vector potentials additional medium modifications of composite particles (mass shifts, internal excitations) dissolution of nuclei, Mott effect proton number Z DZ AME neutron number N Cluster Correlations in Dilute Matter and Nuclei - 8

35 Generalized Relativistic Density Functional extension of relativistic mean-field models with density-dependent meson-nucleon couplings selected model features: extended set of constituents: nucleons, light clusters ( 2 H, 3 H, 3 He, 4 He) and heavy nuclei experimental binding energies: AME 2012 (M. Wang et al., Chinese Phys. 36 (2012) 1603) extension: DZ10 predictions (J. Duflo, A.P. Zuker, Phys. Rev. C 52 (1995) R23) considered as quasi-particles with scalar and vector potentials additional medium modifications of composite particles (mass shifts, internal excitations) dissolution of nuclei, Mott effect proton number Z DZ AME neutron number N NN scattering correlations included correct low-density limit, virial EoS thermodynamically consistent approach rearrangement contributions Details: S. Typel et al., Eur. Phys. J. A 50 (2014) 17, Phys. Rev. C 81 (2010) , M.D. Voskresenskaya and S. Typel, Nucl. Phys. A 887 (2012) 42 Cluster Correlations in Dilute Matter and Nuclei - 8

36 Effective Interaction density-dependent meson-nucleon couplings with parametrization DD2, parameters fitted to properties of nuclei S. Typel et al., Phys. Rev. C 81 (2010) meson-nucleon coupling Γ i (ρ) DD2 ω σ ρ vector density ρ [fm -3 ] Cluster Correlations in Dilute Matter and Nuclei - 9

37 Effective Interaction density-dependent meson-nucleon couplings with parametrization DD2, parameters fitted to properties of nuclei S. Typel et al., Phys. Rev. C 81 (2010) neutron matter EoS consistent with limits of chiral EFT(N 3 LO) calculations I. Tews et al., PRL 110 (2013) , T. Krüger et al., PRC 88 (2013) meson-nucleon coupling Γ i (ρ) DD vector density ρ [fm -3 ] ω σ ρ 30 energy per nucleon E/A [MeV] χeft (N 3 LO) DD2 neutron matter symmetric nuclear matter density n [fm -3 ] Cluster Correlations in Dilute Matter and Nuclei - 9

38 Effective Interaction density-dependent meson-nucleon couplings with parametrization DD2, parameters fitted to properties of nuclei S. Typel et al., Phys. Rev. C 81 (2010) neutron matter EoS consistent with limits of chiral EFT(N 3 LO) calculations I. Tews et al., PRL 110 (2013) , T. Krüger et al., PRC 88 (2013) very reasonable nuclear matter parameters n sat = fm 3 a V = MeV K = MeV J = MeV L = MeV meson-nucleon coupling Γ i (ρ) energy per nucleon E/A [MeV] DD vector density ρ [fm -3 ] symmetric nuclear matter χeft (N 3 LO) DD density n [fm -3 ] ω σ ρ neutron matter Cluster Correlations in Dilute Matter and Nuclei - 9

39 Effective Interaction density-dependent meson-nucleon couplings with parametrization DD2, parameters fitted to properties of nuclei S. Typel et al., Phys. Rev. C 81 (2010) neutron matter EoS consistent with limits of chiral EFT(N 3 LO) calculations I. Tews et al., PRL 110 (2013) , T. Krüger et al., PRC 88 (2013) very reasonable nuclear matter parameters n sat = fm 3 a V = MeV K = MeV J = MeV L = MeV L (MeV) H&W LS NL3 TM1 TMA DD2 FSUgold IUFSU SFHo SFHx J (MeV) meson-nucleon coupling Γ i (ρ) energy per nucleon E/A [MeV] DD vector density ρ [fm -3 ] symmetric nuclear matter χeft (N 3 LO) DD density n [fm -3 ] ω σ ρ neutron matter Cluster Correlations in Dilute Matter and Nuclei - 9

40 Neutron Star Matter I conditions: charge neutrality and β equilibrium (preliminary results: parametrisation of mass shifts still under discussion) total charge fraction 0.8 charge fraction Y q T = 0.2 MeV T = 0.4 MeV T = 0.6 MeV T = 0.8 MeV T = 1.0 MeV T = 1.2 MeV T = 1.4 MeV T = 1.6 MeV T = 1.8 MeV T = 2.0 MeV T = 2.2 MeV T = 2.4 MeV baryon density n b [fm -3 ] Cluster Correlations in Dilute Matter and Nuclei - 10

41 Neutron Star Matter I conditions: charge neutrality and β equilibrium (preliminary results: parametrisation of mass shifts still under discussion) total charge fraction mass fraction of heavy nuclei charge fraction Y q T = 0.2 MeV T = 0.4 MeV T = 0.6 MeV T = 0.8 MeV T = 1.0 MeV T = 1.2 MeV T = 1.4 MeV T = 1.6 MeV T = 1.8 MeV T = 2.0 MeV T = 2.2 MeV T = 2.4 MeV heavy nuclei mass fraction X A T = 0.2 MeV T = 0.4 MeV T = 0.6 MeV T = 0.8 MeV T = 1.0 MeV T = 1.2 MeV T = 1.4 MeV T = 1.6 MeV T = 1.8 MeV T = 2.0 MeV T = 2.2 MeV T = 2.4 MeV baryon density n b [fm -3 ] baryon density n b [fm -3 ] Cluster Correlations in Dilute Matter and Nuclei - 11

42 Neutron Star Matter II conditions: charge neutrality and β equilibrium (preliminary results: parametrisation of mass shifts still under discussion) average neutron number average neutron number of heavy nuclei <N> baryon density n b [fm -3 ] average proton number average proton number of heavy nuclei <Z> baryon density n b [fm -3 ] Cluster Correlations in Dilute Matter and Nuclei - 11

43 Neutron Star Matter III conditions: charge neutrality and β equilibrium (preliminary results: parametrisation of mass shifts still under discussion) mass fractions of light nuclei X i = A i n i n B deuteron mass fraction X d H 3-1 H triton mass fraction X t baryon density n b [fm -3 ] baryon density n b [fm -3 ] triton mass fraction X t He T = 0.2 MeV T = 0.4 MeV T = 0.6 MeV T = 0.8 MeV T = 1.0 MeV T = 1.2 MeV T = 1.4 MeV T = 1.6 MeV T = 1.8 MeV T = 2.0 MeV T = 2.2 MeV T = 2.4 MeV He α particle mass fraction X α baryon density n b [fm -3 ] baryon density n b [fm -3 ] Cluster Correlations in Dilute Matter and Nuclei - 12

44 Constraint from Heavy-Ion Collisions emission of light nuclei in heavy-ion collisions at Fermi energies determination of density and temperature S. Kowalski et al. PRC 75 (2007) J. Natowitz et al. PRL 104 (2010) R. Wada et al. PRC 85 (2012) Cluster Correlations in Dilute Matter and Nuclei - 13

45 Constraint from Heavy-Ion Collisions emission of light nuclei in heavy-ion collisions at Fermi energies determination of density and temperature S. Kowalski et al. PRC 75 (2007) J. Natowitz et al. PRL 104 (2010) R. Wada et al. PRC 85 (2012) thermodynamic conditions as in neutrinosphere of cc supernovae ( femtonovae, C. Horowitz) Cluster Correlations in Dilute Matter and Nuclei - 13

46 Constraint from Heavy-Ion Collisions emission of light nuclei in heavy-ion collisions at Fermi energies chemical equilibrium constants of α particles from M. Hempel et al., PRC 91 (2015) determination of density and temperature S. Kowalski et al. PRC 75 (2007) J. Natowitz et al. PRL 104 (2010) R. Wada et al. PRC 85 (2012) thermodynamic conditions as in neutrinosphere of cc supernovae ( femtonovae, C. Horowitz) particle yields chemical equilibrium constants K c [i] = n i /(n Z i p n N i n ) L. Qin et al., PRL 108 (2012) K c [ ] (fm 9 ) Exp. (Qin et al. 2012) ideal gas HS(DD2), no CS, A 4 SFHo, no CS, A 4 LS220, HIC mod., cor. B STOS, HIC mod. SHT(NL3) SHO(FSU2.1) grdf QS T (MeV) Cluster Correlations in Dilute Matter and Nuclei - 13

47 Constraint from Heavy-Ion Collisions emission of light nuclei in heavy-ion collisions at Fermi energies chemical equilibrium constants of α particles from M. Hempel et al., PRC 91 (2015) determination of density and temperature S. Kowalski et al. PRC 75 (2007) J. Natowitz et al. PRL 104 (2010) R. Wada et al. PRC 85 (2012) thermodynamic conditions as in neutrinosphere of cc supernovae ( femtonovae, C. Horowitz) particle yields chemical equilibrium constants K c [i] = n i /(n Z i p n N i n ) L. Qin et al., PRL 108 (2012) mixture of ideal gases/nse description not sufficient medium effects/correlations important K c [ ] (fm 9 ) Exp. (Qin et al. 2012) ideal gas HS(DD2), no CS, A 4 SFHo, no CS, A 4 LS220, HIC mod., cor. B STOS, HIC mod. SHT(NL3) SHO(FSU2.1) grdf QS T (MeV) Cluster Correlations in Dilute Matter and Nuclei - 13

48 Symmetry Energy and Neutron Skins

49 Constraints on Symmetry Energy density dependence of symmetry energy E s (n) in nuclear matter E A (n,β) = E 0(n) + E s (n)β n = n n + n p β = (n n n p )/n Cluster Correlations in Dilute Matter and Nuclei - 14

50 Constraints on Symmetry Energy density dependence of symmetry energy E s (n) in nuclear matter E A (n,β) = E 0(n) + E s (n)β n = n n + n p β = (n n n p )/n symmetry energy at saturation J = E s (n sat ) slope coefficient L = 3n d dn E s n=nsat Cluster Correlations in Dilute Matter and Nuclei - 14

51 Constraints on Symmetry Energy density dependence of symmetry energy E s (n) in nuclear matter E A (n,β) = E 0(n) + E s (n)β n = n n + n p β = (n n n p )/n symmetry energy at saturation J = E s (n sat ) slope coefficient L = 3n d many efforts to determine J = S v and L experimentally dn E s n=nsat χ Lagrangian and Q. Montecarlo Neutron Matter Neutron-Star Neutron Star Data Observations p & α scattering Neutron Skin charge ex. Antiprotonic Atoms Nuclear Model Fit Heavy Ion Collisions Giant Resonances N A scattering Charge Ex. Reactions Energy Levels Parity Violating e-scattering IVGQR Neutron Skin PDR Neutron Skin Mass Mass n p Emission Ratio Isospin Diffusion GDR PDR N Optical Potential Empirical Dipole Polarizability Parity Violating Asymmetry L (MeV) Hebeler et al. PRL105 (2010) and Gandolfi et al. PRC85 (2012) (R) Steiner et al. Astrophys. J. 722 (2010) 33 Lie-Wen Chen et al. PRC 82 (2010) Centelles et al. PRL 102 (2009) Warda et al. PRC 80 (2009) Möller et al. PRL 108 (2012) Danielewicz NPA 727 (2003) 233 Agrawal et al. PRL109 (2012) Famiano et al. PRL 97 (2006) Tsang et al. PRL 103 (2009) Roca-Maza et al. PRC 87 (2013) Roca-Maza et al. PRC (2013), in press Trippa et al. PRC 77 (2008) (R) Klimkiewicz et al. PRC 76 (2007) (R) Carbone et al. PRC 81 (2010) (R) Xu et al. PRC 82 (2010) PREX Collab. PRL (2012) (X. Viñas et al., Eur. Phys. J. A50 (2014) 27) (J.M. Lattimer, Y. Lim, ApJ. 771 (2013) 51) Cluster Correlations in Dilute Matter and Nuclei - 14

52 Symmetry Energy and Neutron Skins of Nuclei correlation: neutron skin thickness r np = S = rn 2 1/2 rp 2 1/2 derivative of neutron matter EoS B.A. Brown, PRL 85 (2000) 5296 S. Typel and B. A. Brown, PRC 64 (2001) Cluster Correlations in Dilute Matter and Nuclei - 15

53 Symmetry Energy and Neutron Skins of Nuclei correlation: neutron skin thickness rnp = S = r 2 n 1/2 r 2 p 1/2 derivative of neutron matter EoS B.A. Brown, PRL 85 (2000) 5296 S. Typel and B. A. Brown, PRC 64 (2001) symmetry energy slope parameter L NL1 NL2 NL3* 0.3 NL3 PK1 NL-SV2 G2 Sk-T4 NL3.s25 PK1.s FSUGold Sk-Rs Ska DD-PC1 DD-ME1 DD-ME2 0.2 rnp (fm) SkM* HFB-17 SkP 0.15 HFB-8 MSk7 v Linear Fit, r = Skyrme, Gogny RMF TM1 SkI5 G1 NL-RA1 PC-F1 NL-SH PC-PK1 SkX Sk-T6 SkI2 RHF-PKA1 SV Sk-Gs RHF-PKO3 208 Pb SkMP SkSM* SIV MSL0 MSkA BCP SLy5 SLy4 D1N D1S SGII L (MeV) (X. Viñas et al., Eur. Phys. J. A50 (2014) 27) Cluster Correlations in Dilute Matter and Nuclei - 15

54 Symmetry Energy and Neutron Skins of Nuclei correlation: neutron skin thickness r np = S = r 2 n 1/2 r 2 p 1/2 derivative of neutron matter EoS B.A. Brown, PRL 85 (2000) 5296 S. Typel and B. A. Brown, PRC 64 (2001) symmetry energy slope parameter L determine L from experimental measurement of r np parity violation in electron scattering PREX@Jefferson Lab, C.J. Horowitz et al., PRC 63 (2001) , PRC 85 (2012) coherent pion photoproduction MAMI@Mainz, C. Tarbert et al., PRL 112 (2014) r np (fm) Linear Fit, r = Skyrme, Gogny RMF SkX Sk-T6 HFB-17 SkM* FSUGold DD-ME1 DD-ME2 SkMP SkSM* SIV MSL0 MSkA Ska DD-PC1 Sk-Rs PK1.s24 G2 Sk-T4 NL3.s25 RHF-PKO3 SkI2 RHF-PKA1 SV Sk-Gs NL3* NL3 PK1 NL-SV2 TM1 SkI5 G1 NL-RA1 PC-F1 NL-SH PC-PK1 NL2 NL HFB-8 MSk7 v090 SkP SGII D1N SLy5 SLy4 BCP 208 Pb D1S L (MeV) (X. Viñas et al., Eur. Phys. J. A50 (2014) 27) Cluster Correlations in Dilute Matter and Nuclei - 15

55 Symmetry Energy and Neutron Skins of Nuclei correlation: neutron skin thickness r np = S = r 2 n 1/2 r 2 p 1/2 derivative of neutron matter EoS B.A. Brown, PRL 85 (2000) 5296 S. Typel and B. A. Brown, PRC 64 (2001) symmetry energy slope parameter L determine L from experimental measurement of r np parity violation in electron scattering PREX@Jefferson Lab, C.J. Horowitz et al., PRC 63 (2001) , PRC 85 (2012) coherent pion photoproduction MAMI@Mainz, C. Tarbert et al., PRL 112 (2014) correlation based on mean-field models, low densities at nuclear surface effects of correlations? r np (fm) HFB-8 MSk7 v090 SkP D1S Linear Fit, r = Skyrme, Gogny RMF SkX Sk-T6 HFB-17 SGII D1N SkM* FSUGold DD-ME1 DD-ME2 SLy5 SLy4 SkMP SkSM* SIV MSL0 MSkA BCP Ska DD-PC1 Sk-Rs PK1.s24 G2 Sk-T4 NL3.s25 SkI2 RHF-PKA1 SV Sk-Gs L (MeV) RHF-PKO3 (X. Viñas et al., Eur. Phys. J. A50 (2014) 27) NL3* NL3 PK1 NL-SV2 TM1 SkI5 G1 NL-RA1 PC-F1 NL-SH PC-PK1 NL2 NL1 208 Pb Cluster Correlations in Dilute Matter and Nuclei - 15

56 Application of grdf Model finite temperature grdf calculations in spherical Wigner-Seitz cell, extended Thomas-Fermi approximation without light clusters 10-1 particle number density n i [fm -3 ] A heavy = Z heavy = 62.3 p n e T = 5 MeV n = 0.01 fm -3 Y p = radius r [fm] Cluster Correlations in Dilute Matter and Nuclei - 16

57 Application of grdf Model finite temperature grdf calculations in spherical Wigner-Seitz cell, extended Thomas-Fermi approximation without and with light clusters enhanced cluster probability at surface of heavy nuclei, effects for heavy nuclei in vacuum at zero temperature? particle number density n i [fm -3 ] A heavy = Z heavy = 62.3 p n e T = 5 MeV n = 0.01 fm -3 Y p = 0.4 particle number density n i [fm -3 ] A heavy = Z heavy = 48.2 p n e 2 H 3 H 3 He 4 He T = 5 MeV n = 0.01 fm -3 Y p = radius r [fm] radius r [fm] Cluster Correlations in Dilute Matter and Nuclei - 16

58 Application of grdf Model finite temperature grdf calculations in spherical Wigner-Seitz cell, extended Thomas-Fermi approximation zero temperature: only α-particles relevant density distribution from ground-state wave function (WKB approximation) Cluster Correlations in Dilute Matter and Nuclei - 16

59 Application of grdf Model finite temperature grdf calculations in spherical Wigner-Seitz cell, extended Thomas-Fermi approximation zero temperature: only α-particles relevant density distribution from ground-state wave function (WKB approximation) variation with neutron excess of nuclei chain of Sn nuclei Cluster Correlations in Dilute Matter and Nuclei - 16

60 Application of grdf Model finite temperature grdf calculations in spherical Wigner-Seitz cell, extended Thomas-Fermi approximation zero temperature: only α-particles relevant density distribution from ground-state wave function (WKB approximation) variation with neutron excess of nuclei chain of Sn nuclei variation of isovector interaction modified parametrizations, 208 Pb nucleus parametrization symmetry slope ρ-meson ρ-meson energy coefficient coupling parameter J [MeV] L [MeV] Γ ρ (n ref ) a ρ DD DD DD DD DD DD [ )] Γρ(n) = Γρ(n ref )exp aρ( n n 1 ref Cluster Correlations in Dilute Matter and Nuclei - 16

61 Application of grdf Model finite temperature grdf calculations in spherical Wigner-Seitz cell, extended Thomas-Fermi approximation zero temperature: only α-particles relevant density distribution from ground-state wave function (WKB approximation) variation with neutron excess of nuclei chain of Sn nuclei variation of isovector interaction modified parametrizations, 208 Pb nucleus parametrization symmetry slope ρ-meson ρ-meson energy coefficient coupling parameter J [MeV] L [MeV] Γ ρ (n ref ) a ρ DD DD DD DD DD DD energy per neutron E/A [MeV] DD2 +++ DD2 ++ DD2 + DD2 DD2 - DD2 - - neutron matter [ )] Γρ(n) = Γρ(n ref )exp aρ( n n 1 ref S. Typel, PRC 89 (2014) neutron density n [fm -3 ] Cluster Correlations in Dilute Matter and Nuclei - 16

62 Neutron Skin of Sn Nuclei neutron and protons rms radii r n and r p neutron skin thickness r skin = r n r p neutron (proton) rms radius r n (r p ) [fm] neutrons (without α correlations) protons (without α correlations) neutron skin thickness r skin [fm] without α correlations mass number A mass number A Cluster Correlations in Dilute Matter and Nuclei - 17

63 Neutron Skin of Sn Nuclei neutron and protons rms radii r n and r p neutron skin thickness r skin = r n r p neutron (proton) rms radius r n (r p ) [fm] neutrons (without α correlations) neutrons (with α correlations) protons (without α correlations) protons (with α correlations) neutron skin thickness r skin [fm] without α correlations with α correlations mass number A mass number A Cluster Correlations in Dilute Matter and Nuclei - 17

64 Neutron Skin of Sn Nuclei neutron and protons rms radii r n and r p neutron skin thickness r skin = r n r p effective α-particle number N α neutron effective (proton) number rms of radius α-particles r n (r p ) N α [fm] neutrons (without α correlations) neutrons (with α correlations) protons (without α correlations) protons (with α correlations) neutron skin thickness r skin [fm] without α correlations with α correlations mass number A mass number A Cluster Correlations in Dilute Matter and Nuclei - 17

65 Neutron Skin of 208 Pb dependence on symmetry energy slope coefficient L use parametrizations DD2 +++,..., DD RH without α correlations neutron skin thickness r skin [fm] slope coefficient L [MeV] Cluster Correlations in Dilute Matter and Nuclei - 18

66 Neutron Skin of 208 Pb dependence on symmetry energy slope coefficient L use parametrizations DD2 +++,..., DD2 relativistic Hartree (RH) calculation used in original fit of model parameters (correlation r skin L not linear because no complete refit of model parameters, only of effective isovector interaction) neutron skin thickness r skin [fm] RH without α correlations slope coefficient L [MeV] Cluster Correlations in Dilute Matter and Nuclei - 18

67 Neutron Skin of 208 Pb dependence on symmetry energy slope coefficient L use parametrizations DD2 +++,..., DD2 relativistic Hartree (RH) calculation used in original fit of model parameters relativistic Thomas-Fermi (RTF) calculation for description of nuclei with generalized relativistic density functional underestimate of neutron skin thickness but similar correlation as in RH calculation neutron skin thickness r skin [fm] RH without α correlations RTF without α correlations slope coefficient L [MeV] Cluster Correlations in Dilute Matter and Nuclei - 18

68 Neutron Skin of 208 Pb dependence on symmetry energy slope coefficient L use parametrizations DD2 +++,..., DD2 relativistic Hartree (RH) calculation used in original fit of model parameters relativistic Thomas-Fermi (RTF) calculation for description of nuclei with generalized relativistic density functional underestimate of neutron skin thickness but similar correlation as in RH calculation neutron skin thickness r skin [fm] RH without α correlations RTF without α correlations RTF with α correlations slope coefficient L [MeV] with α-particles at surface reduction of neutron skin consequences for determination of L from r skin measurements? Cluster Correlations in Dilute Matter and Nuclei - 18

69 Experimental Study of α-clustering at Nuclear Surface clean probe for α-particles in nuclei: quasi-free (p,pα) knockout reactions Cluster Correlations in Dilute Matter and Nuclei - 19

70 Experimental Study of α-clustering at Nuclear Surface clean probe for α-particles in nuclei: quasi-free (p,pα) knockout reactions experiment at RCNP Cyclotron Facility, Osaka, Japan collaboration with T. Aumann (TU Darmstadt), T. Uesaka (RIKEN) et al. proposal accepted in PAC evaluation March 2014, experiment in June 2015 Cluster Correlations in Dilute Matter and Nuclei - 19

71 Experimental Study of α-clustering at Nuclear Surface clean probe for α-particles in nuclei: quasi-free (p,pα) knockout reactions experiment at RCNP Cyclotron Facility, Osaka, Japan collaboration with T. Aumann (TU Darmstadt), T. Uesaka (RIKEN) et al. proposal accepted in PAC evaluation March 2014, experiment in June MeV proton beam targets: 112 Sn, 116 Sn, 120 Sn, 124 Sn proton detection: Grand Raiden α detection: LAS several spectrometer settings p Sn α Cluster Correlations in Dilute Matter and Nuclei - 19

72 Experimental Study of α-clustering at Nuclear Surface clean probe for α-particles in nuclei: quasi-free (p,pα) knockout reactions experiment at RCNP Cyclotron Facility, Osaka, Japan collaboration with T. Aumann (TU Darmstadt), T. Uesaka (RIKEN) et al. proposal accepted in PAC evaluation March 2014, experiment in June MeV proton beam targets: 112 Sn, 116 Sn, 120 Sn, 124 Sn proton detection: Grand Raiden α detection: LAS several spectrometer settings experimental signatures: dependence of effective α-particle number ( cross sections) on neutron excess N Z localisation of α-particles on surface of nucleus broad momentum distribution p Sn α Cluster Correlations in Dilute Matter and Nuclei - 19

73 Conclusions and Outlook

74 Conclusions and Outlook nuclear/stellar matter: correlations in many-body system essential clustering, modification of chemical composition Cluster Correlations in Dilute Matter and Nuclei - 20

75 Conclusions and Outlook nuclear/stellar matter: correlations in many-body system essential clustering, modification of chemical composition generalized relativistic density functional extension of RMF models with density-dependent couplings, well-constrained parameters extended set of constituents: explicit cluster degrees of freedom, quasiparticle description medium-dependent properties of composite particles formation and dissolution of clusters, correct limits Cluster Correlations in Dilute Matter and Nuclei - 20

76 Conclusions and Outlook nuclear/stellar matter: correlations in many-body system essential clustering, modification of chemical composition generalized relativistic density functional extension of RMF models with density-dependent couplings, well-constrained parameters extended set of constituents: explicit cluster degrees of freedom, quasiparticle description medium-dependent properties of composite particles formation and dissolution of clusters, correct limits applications: equation of state of stellar matter astrophysical simulations nuclear structure reduction of neutron skin Cluster Correlations in Dilute Matter and Nuclei - 20

77 Conclusions and Outlook nuclear/stellar matter: correlations in many-body system essential clustering, modification of chemical composition generalized relativistic density functional extension of RMF models with density-dependent couplings, well-constrained parameters extended set of constituents: explicit cluster degrees of freedom, quasiparticle description medium-dependent properties of composite particles formation and dissolution of clusters, correct limits applications: equation of state of stellar matter astrophysical simulations nuclear structure reduction of neutron skin future: minor improvements of model preparation of global EoS table experimental study of α-particle correlations on surface of Sn nuclei experiment with quasifree (p,pα) reactions at RCNP Osaka extension with quarks hadron-quark phase transition Cluster Correlations in Dilute Matter and Nuclei - 20

78 Thanks to my collaborators Sofija Antić (GSI Darmstadt) Niels-Uwe Bastian (Uniwersytet Wroc lawski) David Blaschke (Uniwersytet Wroc lawski) Tobias Fischer (Uniwersytet Wroc lawski) Matthias Hempel (Universität Basel) Jaroslava Hrtánková (CTU Praha) Thomas Klähn (Uniwersytet Wroc lawski) Micaela Oertel (LUTH Meudon) Gevorg Poghosyan (KIT Karlsruhe) Gerd Röpke (Universität Rostock) Maria Voskresenskaya (GSI Darmstadt) Hermann Wolter (Ludwig Maximilians-Universität München) for support from organizers of WBEN to you, the audience, for your attention and patience Cluster Correlations in Dilute Matter and Nuclei - 21