The National Superconducting Cyclotron State University

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1 HIC Observables to probe the ASY-EOS Betty Tsang The National Superconducting Cyclotron State University

2 Tests of the ASY-EOS in Heavy Ion Collisions asystiff asysoft Tsang, HW BA Li, HW Tsang Di Toro Aumann, Ducoin Low density/energy fragments, ratios isospin diffusion isoscaling migration/fractionat. collective excitations High density/energy differential flow n/p, LIF ratios pions ratios kaon ratios neutron stars QF Li, Di Toro Di Toro, Lukasic DiToro, Reisdorf, QF Li Prassa, QF Li BA Li, Kubis Danielewicz Lehaut surface phenomena phase transitions Hermann Wolter

3 Experimental Observables to probe the symmetry energy E/A(, ) = E/A(,0) + 2 S( ) ; = ( n - p )/ ( n + p ) = (N-Z)/A Low densities ( < 0 ): Isoscaling with statistical models Isospin diffusion n/p spectra and flows; R(n/p), R(t/3He) Fragment isotopic distributions, R(N/Z) Correlation function, C(q) Neutron, proton radii, E1 collective modes. High densities ( 2 0 ) (Reisdorf, Lemmon, Bickley) Neutron/proton, t/ 3 He spectra and flows; C(q) + vs. - production, k, hyperon production.

4 Experimental Observables to probe the symmetry energy E/A(, ) = E/A(,0) + 2 S( ) ; = ( n - p )/ ( n + p ) = (N-Z)/A Low densities ( < 0 ): Isoscaling with statistical models Isospin diffusion n/p spectra and flows; R(n/p), R(t/3He) Fragment isotopic distributions, R(N/Z) Correlation function, C(q) Neutron, proton radii, E1 collective modes. High densities ( 2 0 ) (Reisdorf, Lemmon, Bickley) Neutron/proton, t/ 3 He spectra and flows; C(q) + vs. - production, k, hyperon production.

5 Statistical Multifragmentation Model (SMM) Single source: (Ao, Zo), E*, chemical potentials symmetry energy Grand Canonical Approximation Time Dependence --Initial compression and energy deposition -- Expansion -- Cooling -- Disassembly and freezeout =4C sym [(Z 1 /A 1 ) 2 - (Z 2 /A 2 ) 2 ]/T Tsang et al. PRC 64, (2002)

6 =4C sym [(Z 1 /A 1 ) 2 - (Z 2 /A 2 ) 2 ]/T C sym is adjusted to reproduce experimental B a A a A Z( Z 1) a C A 2/3 V S 1/ 3 ( A 2Z) A C sym 2 C sym closely inter-related to the binding energy

7 B a A a A Z( Z 1) a C A 2/3 V S 1/ 3 ( A 2Z) A C sym 2 Best fit C sym is closely inter-related to the binding energy

8 B a A a A Z( Z 1) a C A 2/3 V S 1/ 3 ( A 2Z) A C sym 2 C sym =22.4 ( a V sym A a S sym 2/3 A ) ( a V sym A a S sym 2/3 A )

9 B a A a A Z( Z 1) a C A 2/3 V S 1/ 3 ( A 2Z) A C sym 2 C sym =22.4 ( a V sym A a S sym 2/3 A ) 2 a / b ) 1/ A ( a 3 2 a / b ) 1/ A ( a 3 ( a V sym A a S sym 2/3 A ) Souza et al, arxiv:0804,1352 Reduction of values can be accomplished with more accurate mass formula rather than to change C sym values obtained from fitting empirical masses!

10 Questionable comparisons! E int =E sym -E KE SMM describes finite nuclei Shetty et al, PRC 76, (2007)

11 Experimental Observables to probe the symmetry energy E/A(, ) = E/A(,0) + 2 S( ) ; = ( n - p )/ ( n + p ) = (N-Z)/A Low densities ( < 0 ): Isoscaling with statistical models Isospin diffusion n/p spectra and flows; R(n/p), R(t/3He) Fragment isotopic distributions, R(N/Z) Correlation function, C(q) Neutron, proton radii, E1 collective modes. High densities ( 2 0 ) Neutron/proton spectra and flows; C(q) + vs. - production, k, hyperon production.

12 Isospin transport Tsang et al. PRL 92, (2004) g i =2; stiff E sym =12.7( / o ) 2/3 + S int ( / o ) gi stiff... soft SKM; soft Diffusion occurs within 120 fm/c. Observable related to of the projectile/target residue More mixing with soft S( ) large E sym at < 0. Less mixing with stiff S( )

13 Isospin transport E sym =12.7( / o ) 2/3 + S int ( / o ) gi stiff soft Tsang et al. PRL 92, (2004) Diffusion occurs within 120 fm/c. Observable related to of the projectile/target residue More mixing with soft S( ) large E sym at < 0. Less mixing with stiff S( )

14 Constraints from Isospin Diffusion Data from one set of data with one set of calculation! M.B. Tsang et. al., PRL 92, (2004)

15 Constraints from Isospin Diffusion Data from one set of data with one set of calculation! M.B. Tsang et. al., PRL 92, (2004) L.W. Chen, C.M. Ko, and B.A. Li, PRL 94, (2005)

16 Constraints from Isospin Diffusion Data from one set of data with one set of calculation! M.B. Tsang et. al., PRL 92, (2004) L.W. Chen, C.M. Ko, and B.A. Li, PRL 94, (2005) C.J. Horowitz and J. Piekarewicz, PRL 86, 5647 (2001) B.A. Li and A.W. Steiner, nucl-th/ Need more and different data sets!

17 MSU+INFN, LNS Catania 124 Sn+ 124 Sn, 124 Sn+ 112 Sn, 112 Sn+ 124 Sn, 112 Sn+ 112 Sn at E/A=35 MeV Chimera array Lower energy Longer interaction times, more N/Z equilibrations

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19 Reasonable agreement with ImQMD predictions Energy loss parameter as an alternative to b?

20 Experimental Observables to probe the symmetry energy E/A(, ) = E/A(,0) + 2 S( ) ; = ( n - p )/ ( n + p ) = (N-Z)/A Low densities ( < 0 ): Isoscaling with statistical models Isospin diffusion n/p spectra and flows; R(n/p), R(t/3He) Fragment isotopic distributions, R(N/Z) Correlation function, C(q) Neutron, proton radii, E1 collective modes. High densities ( 2 0 ) Neutron/proton spectra and flows; C(q) + vs. - production, k, hyperon production.

21 Double Ratio Double Ratio n/p Double Ratios (central collisions) 124 Sn+ 124 Sn;Y(n)/Y(p) 112 Sn+ 112 Sn;Y(n)/Y(p) minimize systematic errors Center of mass Energy Famiano et al. RPL 97 (2006) Effect is much larger than IBUU04 predictions inconsistent with conclusions from isospin diffusion data.

22 Double Ratio Double Ratio n/p Double Ratios (central collisions) 124 Sn+ 124 Sn;Y(n)/Y(p) 112 Sn+ 112 Sn;Y(n)/Y(p) minimize systematic errors Tsang et al. PRL 92, (2004) more accurate measurements Famiano et al. RPL 97 (2006) Center of mass Energy

23 Double Ratio Double Ratio n/p Double Ratios (central collisions) 124 Sn+ 124 Sn;Y(n)/Y(p) 112 Sn+ 112 Sn;Y(n)/Y(p) minimize systematic errors Famiano et al. RPL 97 (2006) Center of mass Energy Calculations are sensitive to models and/or model input parameters: g i, S int, MD effects, NN collisions, isospin effects in NN cross-sections, effective n and p mass.

24 Experimental Observables to probe the symmetry energy E/A(, ) = E/A(,0) + 2 S( ) ; = ( n - p )/ ( n + p ) = (N-Z)/A Low densities ( < 0 ): Isoscaling with statistical models Isospin diffusion n/p spectra and flows; R(n/p), R(t/3He) Fragment isotopic distributions, R(N/Z) Correlation function, C(q) Neutron, proton radii, E1 collective modes. High densities ( 2 0 ) Neutron/proton spectra and flows; C(q) + vs. - production, k, hyperon production.

25 t/ 3 He Double Ratios (central collisions) Double Ratio 124 Sn+ 124 Sn;Y(t)/Y( 3 He) 112 Sn+ 112 Sn;Y(t)/Y( 3 He) minimize systematic errors

26 Center of mass energy spectra for t and 3 He

27 Y(t)/Y( 3 He) single ratios Low energy rise comes from Coulomb effects not properly taken into account in models.

28 t/t & 3 He/ 3 He ratios to minimize Coulomb effects ImQMD code reproduces the overall magnitudes of the effects but sensitivity to g i decreases. Need more theoretical study

29 Double Ratio Comparison of n/p and t/ 3 He double ratios Center of mass Energy At E/A=50 MeV, it is difficult to extend Y(t) and Y( 3 He) to energy > 40 MeV. Significant cluster and sequential decay effects at low energy!

30 Experimental Observables to probe the symmetry energy E/A(, ) = E/A(,0) + 2 S( ) ; = ( n - p )/ ( n + p ) = (N-Z)/A Low densities ( < 0 ): Isoscaling with statistical models Isospin diffusion n/p spectra and flows; R(n/p), R(t/3He) Fragment isotopic distributions, R(N/Z) Correlation function, C(q) Neutron, proton radii, E1 collective modes. High densities ( 2 0 ) Neutron/proton spectra and flows; C(q) + vs. - production, k, hyperon production.

31 Complementary to n/p ratio info. Effects of N/Z ratios for IMF s (3 Z i 8) are small! Differences due to sequential decays? 3 Zi 8 Colonna et al. arxiv:

32 Sequential decay effects are significant Data are more consistent with iso-stiff 3 Zi 8 Colonna et al. arxiv:

33 Double Ratio Double ratios do not eliminate sequential decay effects Sensitivity to iso-eos is much reduced! 124 Sn+ 124 Sn/ 112 Sn+ 112 Sn; E/A=50 MeV primary secondary decays data Colonna et al. arxiv:

34 New Observable : shifted DR KE slope of N/Z E/A=50 MeV ini Data are more consistent with iso-stiff

35 E/A=50 MeV ini Is DRs(N/Z) a robust observable?

36 Experimental Observables to probe the symmetry energy E/A(, ) = E/A(,0) + 2 S( ) ; = ( n - p )/ ( n + p ) = (N-Z)/A Low densities ( < 0 ): Isoscaling with statistical models Isospin diffusion n/p spectra and flows; R(n/p), R(t/3He) Fragment isotopic distributions, R(N/Z) Correlation function, C(q) Neutron, proton radii, E1 collective modes. High densities ( 2 0 ) Neutron/proton spectra and flows; C(q) + vs. - production, k, hyperon production.

37 Isospin effects in Two-proton sources Central collisions Verde et al, Preliminary Sources Preliminary p-p correlation is larger for the n-rich system

38 1+R(q) Source shape and Asy-EOS S(r) (a.u.) neutron-neutron IBUU: 52 Ca+ 48 Ca E/A=80 MeV Asy-soft r 1/2 ~4.4 fm p-p Sources Asy-stiff r 1/2 ~3.6 fm proton-proton proton-neutron r (MeV/c) Asy-soft: larger source, longer proton emission times Verde, Preliminary q (MeV/c) Measure at q<15 MeV/c required!

39 Experimental Observables to probe the symmetry energy E/A(, ) = E/A(,0) + 2 S( ) ; = ( n - p )/ ( n + p ) = (N-Z)/A Low densities ( < 0 ): Isoscaling with statistical models Isospin diffusion n/p spectra and flows; R(n/p), R(t/3He) Fragment isotopic distributions, R(N/Z) Correlation function, C(q) Neutron, proton radii, E1 collective modes. High densities ( 2 0 ) Neutron/proton spectra and flows; C(q) + vs. - production, k, hyperon production.

40 Double Ratio SUMMARY I: Models should explain all experimental observables: isospin diffusions, rapidity and impact parameter dependence, n/p ratios, N/Z ratios etc Model Uncertainties Center of mass Energy

41 SUMMARY II: New data, new challenges

42 Double Ratio SUMMARY III: Alternatives to n/p ratios? Require theoretical understanding of cluster formations and more accurate treatment of Coulomb! Center of mass Energy Promising observable N/Zs(IMF). How robust? ini

43 SUMMARY IV : We are making progress in determining the asy-eos at low density both experimentally and theoretically. Do we have enough information to assign g value? Brown, PRL 85 (2000) 5296 Neutron matter EOS? Chen et al. PRC 72 (2005) Fragment observables eliminate very soft asy-eos at low density.

44 Acknowledgements Theorists: W. Friedman (Wisconsin, Madison) P. Danielewicz (MSU), S. Das Gupta (McGill, Canada), A. Ono (Tokohu, Japan), B.A. Li, (Texas), L. Shi (MSU), Y.X. Zhang (China), S. Souza (Brazil), Colonna (INFN) Experimentalists: HiRA collaboration Michigan State University D. Coupland, T.X. Liu (thesis), M. Famiano (n/p expt), W.G. Lynch, Z.Y. Sun, W.P. Tan, G. Verde, A. Wagner, H.S. Xu, Washington University L.G. Sobotka, R.J. Charity Inidiana University R. desouza, V. E. Viola

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46 Summary V: Need systematic study of transport parameters dependence on symmetry energy to resolve the inconsistencies between models and experimental data and to provide better constraints on the density dependence of the symmetry energy Danielewicz, Lacey, Lynch, Science 298,1592 (2002) Results obtained in transport model simulations of Au+Au collisions to reproduce the flow (E/A~1-8 GeV) measurements. Transport models include constraints in momentum dependence of the mean field and NN crosssections

47 Impact Parameter dependence of R 7 is different from 35 to 50 MeV

48 Effects of momentum dependence of the mean field MI MD z (fm) Larger neck fragments are formed when momentum dependence of the mean field is considered. What is the effect of MD on isospin diffusion? z (fm) Coupland, 2008

49 Isospin Diffusion--Isospin Transport Ratio Isospin diffusion occurs only in asymmetric systems A+B No isospin diffusion between 124 symmetric systems 124 R Non-isospin diffusion effects i = 1 same for A in A+B & A+A ;same for B in B+A & B+B R i 2 AB ( AA AA BB BB ) / x AB, AB experimental or theoretical observable for AB x AB = a AB +b R i (x AB )= R i ( AB ) Rami et al., PRL, 84, 1120 (2000) Observables: AB, AB (isoscaling), ln(y( 7 Li)/Y( 7 Be)) R i = -1

50 y/y beam R 7 R i ( )=R i ( ) R 7 isoscaling BUU

51 MI SUMMARY IV: MD z (fm) Systematic study of transport parameters dependence on symmetry energy z (fm) Coupland, 2008

52 0 Emission patterns of 7 Li & 7 Be from 124 Sn+ 112 Sn; E/A=50 MeV CM V // Y( 7 Li) enhanced from 124 Sn Y( 7 Be) enhanced from 112 Sn

53 Y( 7 Li) enhanced from 124 Sn 112 Sn+ 124 Sn V // (au)

54 Y( 7 Li) enhanced from 124 Sn 112 Sn+ 124 Sn Y( 7 Be) enhanced from 112 Sn V // (au)

55 Y( 7 Li) enhanced from 124 Sn 112 Sn+ 124 Sn Y( 7 Be) enhanced from 112 Sn Ratio Y( 7 Li)/Y( 7 Be) Mainly dominated by Coulomb V // (au) How to observe isospin transport? R i x 2 AB x xaa x AA BB x BB

56 Isospin Transport Ratio 112 Sn+ 124 Sn x=ln(y( 7 Li)/Y( 7 Be) R i x 2 AB x xaa x AA BB x Coulomb & other (preequilibrium & sequential) effects are cancelled BB Liu et al., PRC, 84, 1120 (2006)

57 Constraining the EOS at high densities by laboratory collisions pressure contours density contours The blocking by the spectator matter provides a clock with which to measure the expansion rate.

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