M. Valentina Ricciardi GSI, Darmstadt

1. THE ROLE OF NUCLEAR-STRUCTURE EFFECTS IN THE STUDY OF THE PROPERTIES OF HOT NUCLEAR MATTER M. Valentina Ricciardi GSI, Darmstadt

2. PROPERTIES OF HOT NUCLEAR MATTER Multifragmentation  establishing the caloric curve Heat bath at temperature T T can be deduced from measured yields Yield ~ e-E/T Assumption: thermodynamic equilibrium light fragments investigated

3. MOVING TOWARDS HEAVIER FRAGMENTS Very precise production cross-sections on the entire production range (from high-resolution magnetic spectrometers) 58,64Ni on Be at 140 A MeV A1900, NSCL, MSU, Michigan, U.S.A. M. Mocko et al., Phys. Rev. C 74 (2006) 054612 56Fe on Ti at 1000 A MeV FRS, GSI, Darmstadt, Germany P. Napolitani et al., Phys. Rev. C 70 (2004) 054607

4. COMPLEX EVEN-ODD EFFECT IN THE YIELDS 56Fe on Ti at 1000 A MeVP. Napolitani et al., Phys. Rev. C 70 (2004) 054607 binary decay excluded! Same complex behavior observed in a large bulk of new data. Observed for the first time already in 2003 for 238U on Ti at 1 A GeVM. V. Ricciardi et al., Nucl. Phys. A 733 (2003) 299

5. FOLLOWING THE FOOTPRINTS OF THE DATA... Light multifragmentation products: Yield ~ e-E/T Let us assume that evaporation does not play any role  the staggering in the yields should be correlated to that in binding energies

6. FOLLOWING THE FOOTPRINTS OF THE DATA... Light multifragmentation products: Yield ~ e-E/T Let us assume that evaporation does not play any role  the staggering in the yields should be correlated to that in binding energies N=Z Production cross sections (mb) for 56Fe on Ti at 1 A GeV Staggering in binding energy (MeV) (BEexp from Audi Wapstra – BEcalc from pure LDM Myers, Swiatecky)

7. FOLLOWING THE FOOTPRINTS OF THE DATA... Light multifragmentation products: Yield ~ e-E/T Let us assume that evaporation does not play any role  the staggering in the yields should be correlated to that in binding energies N=Z N=Z+1 ? Production cross sections (mb) for 56Fe on Ti at 1 A GeV Staggering in binding energy (MeV) (BEexp from Audi Wapstra – BEcalc from pure LDM Myers, Swiatecky)

8. 0 ½ 0 ½ 0 ½ 0 ½ 0½ ½ 1 ½ 1 ½ 1 ½ 2½ 1 0 ½ 0 ½ 0 ½ 0½ 0 ½ ½ 1 ½ 1 ½ 2½ 1 ½ 1 0 ½ 0 ½ 0½ 0 ½ 0 ½ ½ 1 ½ 2½ 1 ½ 1 ½ 1 0 ½ 0½ 0 ½ 0 ½ 0 ½ ½ 2½ 1 ½ 1 ½ 1 ½ 1 0½ 0 ½ 0 ½ 0 ½ 0 ½ OVERVIEW ON THE STAGGERING IN THE BINDING ENERGY Extra binding energy associated with the presence of congruent pairs: (Myers Swiatecki NPA 601, 1996, 141) most bound less bound N=Z N=Z+1 o e staggering in the ground-state energies o e o e It is not the binding energy responsible for the staggering in the cross sections o e e o e o e o e o e o

9. UNDERSTANDING THE STAGGERING IN THE YIELDS What if the fragments are the residues of an evaporation cascade?  structures in the yield appear as the result of the condensation process of heated nuclear matter while cooling down in the evaporation process. Pairing is restored in the last evaporation step(s)

10. UNDERSTANDING THE STAGGERING IN THE YIELDS Last step in the evaporation cascade o.o. o.e. o.e. /e.o. o.o. /e.e e.e. e.o.

11. THE KEY ROLE OF THE SEPARATION ENERGY "Energy range" = min(Sn, Sp) keV data from Audi-Wapstra

12. THE KEY ROLE OF THE SEPARATION ENERGY data from Audi-Wapstra

13. THE KEY ROLE OF THE SEPARATION ENERGY Sequential evaporation plays a decisive role data from Audi-Wapstra

14. STAGGERING IN YIELDS VERSUS min(Sn,Sp) cross sections cross sections particle threshold particle threshold binding energies binding energies N=Z N=Z+1 Production cross sections 56Fe+Ti 1 A GeV (mb) Staggering in binding energy (MeV) Particle threshold = lowest Sn Sp particle separation energy (MeV) The lowest particle separation energy reproduces qualitatively the staggering  the sequential de-excitation process plays a decisive role!

15. SUMMARISING THIS SIMPLE IDEA • It concerns residual products (yields) – from any reaction – which passed through at least one evaporation step • Even-odd staggering is complex even qualitatively • The complex behavior of the even-odd staggering can be reproduced qualitatively by the lowest separation energy (threshold energy) • J. Hüfner, C. Sander and G. Wolschin, Phys. Let. 73 B (1978) 289. • X. Campi and J. Hüfner, Phys. Rev. C 24 (1981) 2199. Now we want to apply this simple idea...

16. 1st APPLICATION: THIS IDEA IN A STATISTICAL DEEXCITATION MODEL • We take a statistical model without structural effects (pure LDM) • Once the "pre-fragment" enters into the last evaporation step (E* < Elast) we stop the statistical treatment • We treat the last evaporation step with the "threshold method" (deterministic) THRESHOLD METHOD (E* < Elast) Pre-fragment: N,Z Final fragment If E* lower than Sn, Sp+Bp and S+B Gamma emission N, Z If Sn lower than Sp+Bp and S+B Neutron emission N-1, Z If Sp+Bp lower than Sn and S+B Proton emission N, Z-1 If S+B lower then Sn and Sp+Bp  Alpha emission N-2, Z-2

17. COMPLEX EVEN-ODD EFFECT IN THE YIELDS 56Fe on Ti at 1000 A MeVP. Napolitani et al., Phys. Rev. C 70 (2004) 054607

18. RESULTS: 56Fe on Ti at 1000 A MeV Experiment ABRABLA07 (LDM) + Threshold method

19. RESULTS: 56Fe on Ti at 1000 A MeV Experiment ABRABLA07 (LDM) + Threshold method

20. 56Fe on Ti at 1000 A MeV Comparison experiment vs. ABRABLA07 (LDM) + Threshold method • Qualitatively: good result  n and p evaporation are dominant • Quantitatively: too strong staggering • Possible reasons: • competition between n, p, a decay occurs in specific cases for light nuclei, i.e. level density plays a role (see talk M. D'Agostino) • indications that the pre-fragment distribution in the last evaporation step is not smooth (see talk M. D'Agostino) • influence of unstable states (see talk M. D'Agostino) • influence of the fluid-superfluid phase transition (some additional E* is gained from the formation of pairs)

21. TRUE ABRABLA07

22. TRUE ABRABLA07

23. 2nd APPLICATION: THE ODD-EVEN Z ISOSPIN ANOMALY L. B. Yang et al., PRC 60 (1999) 041602 Elemental even-odd effect decreases with increasing neutron-richness of the system. This fact is also reflected in this figure: N/Z = 1.07 N/Z = 1.23

24. OBSERVED IN MANY OTHER SYSTEMS Winchester et al., PRC 63 (2000) 014601 E. Geraci et al. NPA 732 (2004) 173 Y(112Sn + 58Ni) Y(124Sn + 64Ni) at 35 A MeV 40Ca158Ni/40Ca158Fe 40Ar158Ni/40Ar158Fe 25 MeV/nucleon K.X.Jing et al., NPA 645 (1999) 203 78Kr+12C90Mo, 82Kr+12C94Mo T.S. Fan et al., NPA 679 (2000) 121 58Ni+12C70Se, 64Ni+12C76Se Jean-Pierre Wieleczko, GANIL, 78,82Kr +40Ca at 5.5 MeV , this conference MSU? Texas?

25. OBSERVED AT FRS EXPERIMENTS, GSI 136,124Xe + Pb at 1 A GeV D. Henzlova et al., PRC 78, (2008) 044616 124Xe136Xe Elemental even-odd effect decreases with increasing neutron-richness of the system. We want to explain this fact in a very simple (simplified) way....

26. 1st ASPECT: MEMORY EFFECT 136,124Xe + Pb at 1 A GeV The isotopic distributions are systematically shifted

27. 2nd ASPECT: EVEN-ODD STAGGERING min(Sn, Sp) min(Sn, Sp) keV Z=13 Z=12 The strength of the staggering is stronger along even-Z chains

28. A MATHEMATICAL GAME ...you get two staggering Gaussians... ...you put a staggering... (for Z=even and Z=odd use different intensities) You take two shifted Gaussians... Z=even Z=odd ...the ratio of the integrals staggers!

29. RESULTS: 136,124Xe on Pb at 1000 A MeV

30. RESULTS: 58Ni+58Ni / 58Fe+58Fe at 75 A MeV

31. CONCLUSIONS It is not the binding energy (pure Boltzmann approach) that is responsible for the staggering in the yields The characteristics of the staggering correlate strongly with the lowest n p particle separation energy of the final experimentally observed nuclei. Even the yields of the lightest multifragmentation products (e.g. Li) are governed by evaporation (model independent!). Warning to all methods based on Boltzmann statistics when determining directly (neglecting evaporation) the properties of hot nuclear matter A simple macroscopic statistical model + a deterministic treatment of the last evaporation step based on the lowest Sn Sp can reproduce qualitatively all the characteristics of the even-odd staggering (including even-odd Z isospin anomaly) A good qualitative description of even-odd requires a much larger effort

32. 3rd APPLICATION: ODD-EVEN STAGGERING IN THE <N>/Z OF FRAGMENTS W. Trautmann, NPA 787 (2007) 575c D. Henzlova et al., PRC 78, (2008) 044616 The odd-even in <N>/Z effect is stronger for neutron-poor systems

33. 3rd APPLICATION: ODD-EVEN STAGGERING IN THE <N>/Z OF FRAGMENTS The odd-even in <N>/Z effect is stronger for neutron-poor systems

34. The last evaporation step is calculated by comparing the neutron, proton and alpha separation energies + Coulomb barriers. The last two evaporation steps could be: 1) n --> n Minimum energy = S2n 2) n --> p Minimum energy = Snp 3) n --> alpha Minimum energy = Sna 4) p --> p Minimum energy = S2bp 5) p --> n Minimum energy = Spn 6) p --> alpha Minimum energy = Spa 7) alpha --> alpha Minimum energy = Saa 8) alpha --> n Minimum energy = San 9) alpha --> p Minimum energy = Sap The last evaporation step is defined by the condition: E* < min (S2n , Snp, Sna, S2bp, Spn, Spa, Saa, San, Sap)