Heavy&ion*collisions:*Direct*and*indirect* probes*of*the*density* and*temperature*dependence*of*e sym * * S. Yennello Texas A&M University

Transcription

1 Heavy&ion*collisions:*Direct*and*indirect* probes*of*the*density* and*temperature*dependence*of*e sym * * S. Yennello Texas A&M University

2 Number of ways to measure symmetry energy Direct measurements isoscaling Indirect measurements comparison to statistical or dynamical models Uncertainties temperature, density, secondary decay, source composition

3 Projectile nuclei Reac;on*dynamics*is*sensi;ve* to*e sym (ρ)* stiff soft α Isoscaling parameter A. Ono et al, Phys. Rev. C 68 (2003) (R)

4 Projectile nuclei Experimental*Measurements* 0.5 α Y(Ar + Fe) / Y(Ca + Ni) Y(Fe + Fe) / Y(Ni + Ni) Y(Ar + Ni) / Y(Ca + Ni) Y(Fe + Ni) / Y(Ni + Ni) ELab (MeV/A) 58 Ni, 58 Fe + 58 Ni, 58 30, 40, 47 MeV/A 40 Ar, 40 Ca + 58 Ni, 58 25, 33, 45, 53 MeV/A J. Iglio et al, PRC 74 (2006) , D.V. Shetty et al, PRC 68 (2003)

5 Projectile nuclei Comparison*between*Expt.*&* AMD*Calc.* 1.0 Stiff 0.8 Soft 0.6 α 0.4 Data favors stiff form of E sym (ρ)" Assumption : sequential decay effect between primary & secondary α is small (< 20%)" (Z/A)1 2 - (Z/A)2 2 D. V. Shetty et al, PRC 70 (2004) (R)

6 Comparison*to*the*Esym*(ρ)*from* other*dynamical*studies* D. V. Shetty et al, PRC 70 (2004) (R) L.W. Chen et al, PRL 94 (2005)

7 Comparison*of*MF*data*to*SMM* Secondary fragments Primary fragments D.V. Shetty et al, Phys. PRC 71 (2005)

8 Good agreement between the statistical and the dynamical approach is obtained Sta;s;cal*approach*:** Statistical Dynamical

9 DIT*can*produce*neutron&rich* heavy*residues* ΔA Neutron richness

10 Mass Distribution of Germanium from 86Kr(25MeV/u) + 124Sn,112Sn, 64Ni DIT*can*produce*neutron&rich* heavy*residues* Data using targets: Ge 124 Sn 112 Sn 64 Ni EPAX2 Target N/Z Valley of stability 124 Sn 1.48 n-rich 118 Sn 112 Sn 1.24 n-poor 64 Ni 1.29 n-rich 60 Ni

11 ***Scaling*of*Yield*Ra;os*:* R 21 (N,Z) = Y 2 /Y 1 86 Kr+ 124 Sn, 112 Sn (data inside Θ gr =6.2 ο ) R 21 = C exp ( α N ) 86 Kr+ 64 Ni, 58 Ni (data outside Θ gr =3.5 o )

12 G.A. Souliotis et al, nucl-ex/ (2005) ***Scaling*of*Yield*Ra;os**

13 α = 4C sym /T ( (Z/A) 1 2 (Z/A) 22 ) c 86 Kr,* 64 Ni,* 136 Xe*data:***Isocaling* parameter*α**vs**δ(z/a) 2 :* Quasi-projectiles : E/A ~20-25 MeV N/Z equilibrated, 86 Kr+ 124,112 Sn E* 2.0 MeV/u 86 Kr+ 64,58 Ni E* 2.4 MeV/u 64 Ni+ 124,112 Sn 64 Ni+ 64,58 Ni 64 Ni+ 232 Th, 208 Pb E* 2.9 MeV/u 136 Xe+ 124,112 Sn 136 Xe+ 64,58 Ni 136 Xe+ 232 Th,Au E* 2.5 MeV/u

14 *Varia;on*w.r.t**excita;on*energy:* Data : 86 Kr+ 124,112 Sn 86 Kr+ 64,58 Ni 64 Ni+ Ni,Sn,Th-Pb 136 Xe+Ni,Sn,Th-Au Calculation: Fermi Gas (K=13) Mononucleus expansion model (L. Sobotka, J. Toke) C sym = c T / 4

15 <Z/A>**versus**A*distribu;ons:*** 86 Kr (25 MeV/u) Sn Data DIT/SMM05 Calculations: C sym = 25 MeV C sym = 20 MeV C sym = 15 MeV Stability Line... (EAL) Evap. Attractor 15

16 <Z/A>**vs**A*with*C sym (E*)*** MARS Data DIT/SMM05 (+prox) C sym (E*/A) ( trial form ) ---- C sym (E*/A) ( diagonal test ) 25 Thin lines with θ, Bρ cut. No effect (almost) of the spectrometer acceptance on <N/Z>!!!! The data provide a representative sample of the full distributions

17 Decrease*in*Symmetry*energy** G.A. Souliotis et al., PRC 73 (2006) G.A. Souliotis et al., PRC 75 (2007) R. Ogul et al., Phys. Rev. C 83, (2011). A. Le Fevre et al., PRL 94 (2005) D.V. Shetty et al., PRC 74 (2005)

18 Decrease*due*to*thermal*expansion Finite T Thomas-Fermi Seyler Blanchard interaction B.A. Li et al., PRC 74 (2006) S.K. Samaddar et al., PRC 76 (2007) Data : G.A. Souliotis et al., PRC 73 (2006) D.V. Shetty et al., PRC (2007) D.V. Shetty et al., PRC 76 (2007)

19 System Target N/Z Projectile N/Z 40 Ar+ 112 Sn Ar+ 124 Sn Ca+ 112 Sn Ca+ 124 Sn Ca+ 112 Sn Ca+ 124 Sn and 45 MeV/nucleon Isoscaling*of*fragments*from* reconstructed*quasiprojec;les*

20 System Target N/Z Projectile N/Z (N/Z) CS 40 Ar+ 112 Sn Ar+ 124 Sn Ca+ 112 Sn Ca+ 124 Sn

21 Source 1 Source 2

22 Isoscaling*by*N/Z qp *

23 System*to*system*with*data* from*one*bin*in*n/z qp *

24

25 Isoscaling*parameter*α,*as*a* func;on*of*e**

26 Effect*of*missing*neutrons*on*N/Z qp *

27

28 NIMROD used to add neutrons event by event S. Wuenschel et al., Phys. Rev. C 79, (2009).

29 Comparison*of*Kr*data*with* Ar/Ca*data* Ar/Ca + Sn Kr + Ni

30 C sym * 86 Kr+ 64 Ni, 78 Kr+ 58 Ni Must have T to obtain Csym Natowitz compilation S. Wuenschel, Thesis 2009!

31 Comparison*of*symmetry*energy* as*a*func;on*of*excita;on*energy* 30 SW variable temperature SW T=5.3 MeV 28 Shetty et al, PRC 76, (2007) CSym (MeV) E*(MeV/nucleon)

32 Fluctua;on*Thermometer* Q i = 2* P Z 2 P T 2 For each particle in an event in the reference frame of the source event If T>0 Q does not have to equal zero Fluctuations Q i = 0 Fluctuations provide a variance Changes with E* Can be linked to T

33 Fluctua;on*Thermometer* Protons N/Z bins -> Systems 86 Kr+ 64 Ni, 78 Kr+ 58 Ni Recoil corrected [1]J.B. Natowitz et al. Phys. Rev. C 65 (2002) !

34 Moving*Source*Fiang* Moving source fitting ρ ρ 0 = k k 0 L.G. Moretto Nucl. Phys. A 247, 211 (1975). D. Bracken Thesis Indiana University

35 T T= 8E* T= 13E* Natowitz Kr+ Ni Kr+ Ni Symmetry*energy*as*a* func;on*of*density* * 30 C sym 30 CSym (MeV) C Sym =31.6(ρ/ρ 0 ) 0.69 C Sym with constant T=5.3 MeV C Sym with evolving temperature 1 Viola et al. This data > 0.8 ρ/ρ 0 1MeV 0.6 < / E*/A S. Wuenschel, thesis 2009

36 Comparison of density profile (Be, B, C, N, O) ρ /ρ Viola Source fit Natowitz E*(Me V/nucle on) Viola et al., PRL 93, (2004) Natowitz et al., PRC 66, (R) (2002)

37 IMF*Transverse*Flow* R~1 R~0.0 Mass Dependence Charge Dependence 64 Zn 70 Zn 64 Ni

38 Transverse*collec;ve*flow**&*E sym (ρ)* IMF Flow Comparison to AMD-GEMINI Model! Average Z=4-9! Z. Kohley et al., Phys. Rev. C 82, (2010)

39 Summary* Collec;ve*limits*on*E sym (ρ)* Z. Kohley et al, Phys. Rev. C (2013). M.B. Tsang et al, Phys. Rev. Lett. (2009) D.V. Shetty et al, Phys. Rev. C (2007). P. Russotto et al., Phys. Lett. B (2011). B.A. Li et al, Phys. Rep. (2008). Z. Kohley et al., Phys. Rev. C (2010) Z. Kohley, EPJA, 2013

40 Asymmetry*Dependence*of*the* Nuclear*Caloric*Curve* 48 A QP 52 5 narrow asymmetry bins Larger Asymmetry! Lower Temperature > 1 MeV shift! Evenly Spaced A.B. McIntosh Phys. Lett. B. (2013); Phys Rev C (2013)

41 Summary* Much progress has been made on elucidating the symmetry energy Decreases with E* Largely density driven Consistency across different observables, models Lots of work ahead

42 Acknowledgements* D.*Shedy,*S.*Wuenschel,*S.*Galonopolis,*G.A.*Soulio;s,*Z.* Kohley,*A.*McIntosh,*D.*Rowland,**R.*Dienhoffer,*R.*Tripathi,*L.* May,*K.*Hagel,*R.*Wada,*S.N.*Soisson,*B.C.*Stein,*T.*Fagin,*M.* Mehlman,*W.*B.*Smith*R.*Laforest,*E.*Ramakrishnan,*M.* Veselsky,*E.M.*Winchester,*A.*Ruangma,*E.*Mar;n** A.*Bonasara,*M.*Colonna,*M.*di*Toro,*M.*Zielinksa&Pfabe,*J.* Rizzo,*H.*Wolter,*B.A.*Li,*A.*Botvina,*R.*Charity,*A.*Ono*and*M.* Papa* Funding: Department of Energy National Science Foundation Welch Foundation

43 P. Marini et al., Phys. Rev. C 87, (2013).

44 P. Marini et al., Phys. Rev. C 87, (2013).