EVEN-ODD EFFECT IN THE YIELDS OF NUCLEAR-REACTION PRODUCTS

1. EVEN-ODD EFFECT IN THE YIELDS OF NUCLEAR-REACTION PRODUCTS M. Valentina Ricciardi GSI, Darmstadt, Germany

2. EVEN-ODD EFFECT IN THE YIELDS OF NUCLEAR-REACTION PRODUCTS OUTLINE Experimental evidence of even-odd staggering in the yields: common properties and differences GSI results: a powerful overview Understanding the even-odd staggering Implications for the study of properties of hot nuclear matter Main consequences of our simple idea

3. What we are speaking about We make a nuclear reaction and we observe the final products effect structure staggering zigzag Even-odd Without pairing With pairing

4. Experimental evidence of even-odd staggering in the yields Steinhäuser et al., Nuc. Phys.A 634 (1998) 89 Sl. Cavallaroet al., Phys. Rev. C 57 (1998) 731 low-energy fission 35Cl + 24Mg 8 A MeV C. N. Knottet al., Phys. Rev. C 53 (1996) 347 Ch. O. Bacriet al., Nucl. Phys. A 555 (1998) 477 40Ar + target 44 A MeV 40Ca + p

5. A25 T/MeV gas 5 coexistence liquid 0.5 superfluid E*/MeV 10 70 300 What do yields have in common in all these different reactions? What is different? In common: an even-odd staggering is observed Independent of the reaction mechanism PAIRING is responsible for the even-odd effect Different: the characteristics of the staggering can be different the PHASE through which the nucleus is passing SUPERFLUID The nucleus warms up a bit and cools down without fully exiting the superfluid phase LIQUID The nucleus warms up, enters the liquid phase, then it cools down by evaporation back into the superfluid phase COEXISTENCE LIQUID-GAS The nucleus warms up, experiences a co-existence phase, then the liquid pieces cool down by evaporation back into the superfluid phase

6. SUPERFLUIDITY EVEN-ODD STRUCTURE IN LOW-ENERGY FISSION Zfiss=90 Zfiss=89 Results from e.m.-induced fission of 70 different secondary projectiles (Steinhäuser et al., Nuc. Phys.A 634 (1998) 89 K. H. Schmidt et al., Nucl. Phys. A 665 (2000) 221 ) Conclusion: Structural properties survive at low energy (F. Rejmund et al., Nucl. Phys. A 678 (2000) 215-234)

7. compound nucleus collision E.g.: transfer abrasion cold fragment superfluid de-excitation by fission / evaporation LIQUID PHASE we describe successfully some aspects of the nucleus as a liquid drop Keep in mind! Final nuclei observed in a great variety of nuclear reactions have experienced a de-excitation process (evaporation)! Nuclei pass from the liquid to the superfluid state. Nuclei pass from being "structureless" to "structurefull".

8. Evaporation residues: Which are the characteristics of this type of final yields? C. N. Knottet al., Phys. Rev. C 53 (1996) 347 Ch. O. Bacriet al., Nucl. Phys. A 555 (1998) 477 40Ca + p Yields of nuclei with even Z are enhanced Yields of nuclides with even N=Z number are enhanced Nowadays we can tell much more...

9. A powerful overview: GSI data Use of high-resolution magnetic spectrometers to measure production yields: - full Z, A identification - entire production range - very precise measurement Experimental set-up at the FRagment Separator (FRS), GSI Z from IC: A/Z from time and position:

10. A powerful overview: GSI data Fragmentation data: 1 A GeV 238U on Ti Sequence: N-Z=constant

11. Experimental results for 238U fragmentation ● N=Z■ N=Z+2 ▲N=Z+4 N=Z+6 ● N=Z+1■ N=Z+3▲N=Z+5 Data reveal complex structural effects! M. V. Ricciardi et al., Nucl. Phys. A 733 (2003) 299

12. C. Villagrasa-Canton et al., Phys. Rev. C 75 (2007) 044603 P. Napolitani et al., Phys. Rev. C 70 (2004) 054607 Same complex behavior observed in a large bulk of new data.

13. compound nucleus collision E.g.: transfer abrasion cold fragment withstructure evaporation Can we explain this complex behavior? We have this picture in mind: without structure The compound nucleus is hot and structureless In each evaporation step the mass and excitation energy are reduced. The new compound nucleus is still structureless. Only below Ecritical (~10 MeV) structural effect can exist Below 10 MeV of excitation energy particle evaporation normally stops  we test the idea that pairing is restored in the last evaporation step, i.e. the even-odd effect in the yields is determined in the last evaporation step

14. How does particle evaporation proceeds? The dominant particle-decays in the last evaporation step are n and p emission

15. Understanding the staggering in the yields Last step in the evaporation cascade (assuming only n and p evaporation) o.o. o.e. o.e. /e.o. o.o. /e.e e.e. e.o. The lowest particle separation energy is the key quantity!

16. The key role of the separation energy "Energy range" = "Particle threshold" = min(Sn, Sp) keV data from Audi-Wapstra

17. The key role of the separation energy "Energy range" = "Particle threshold" = min(Sn, Sp) data from Audi-Wapstra The complex features of the even-odd staggering are reproduced in this fishbone pattern!

18. Conclusions concerning the yields from nuclei in the LIQUID PHASE The even-odd staggering of final nuclei which have experienced a de-excitation process (evaporation) is determined in the last evaporation step in other words: Structural properties do not survive in excited nuclei, but the pairing interaction is restored once the nucleus falls below the critical energy The characteristics of the staggering correlate strongly with the lowest n p particle separation energy of the final experimentally observed nuclei.

19. Coexistence liquid-gas Multifragmentation  establishing the caloric curve Heat bath at temperature T Excitation energy: measured from the masses of observed final fragments Temperature: measured from the ratio of the yields of observed final fragments

20. Temperature: a very important variable Heat bath at temperature T The temperature is determined by the Boltzmann factor. The Boltzmann factor is a weighting factor that determines the relative probability of a state i in a multi-state system in thermodynamic equilibrium at temperature T. the ground state has highest probability to be populated Yield ~ e-Ei/kT The ratio of the probabilities of two states is given by the ratio of their Boltzmann factors. Under the assumption that only (mostly) the ground state is populated, T can be deduced from the yields and the binding energies of two final fragments (ISOTOPE THERMOMETER). Using very light final fragments for the thermometer, one hopes that close heavier fragments are also cold and do not evaporate (no SIDE FEEDING). light fragments investigated

21. Even-odd effect in the yields of multifragmentation products 56Fe on Ti at 1000 A MeV P. Napolitani et al., Phys. Rev. C 70 (2004) 054607 We focus now on the very light nuclei, undoubtly attributed to multifragmentation. Let us consider these 2 chains: N=Z even-odd effect N=Z+1 odd-even effect

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

23. 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: most bound less bound e o e o e o e o N=Z N=Z+1 staggering in the ground-state energies (Myers Swiatecki NPA 601, 1996, 141) It is not the binding energy responsible for the staggering in the cross sections e o e o e o e o e o

24. Expected even-odd staggering in evaporation residues FISHBONE PATTERN "Energy range" = min(Sn, Sp) data from Audi-Wapstra

25. Staggering in yields vs. min(Sn,Sp) N=Z+1 N=Z cross sections cross sections particle threshold particle threshold binding energies binding energies Production cross sections (mb) Staggering in binding energy (MeV) Particle threshold = lowest particle separation energy (MeV) The lowest particle separation energy reproduces perfectly the staggering  the sequential de-excitation process plays a dominant role!

26. Conclusions concerning the yields from nuclei in theCOEXISTENCE PHASE The even-odd staggering of final nuclei does not correlate with the binding energy  It is not the binding energy (pure Boltzmann approach) that is responsible for the staggering in the yields of multifragmentation process but the lowest particle separation energy Even the yields of the lightest multifragmentation products (e.g. Li) are governed by evaporation (side feeding is relevant!) Warning to all methods based on Boltzmann statistics when determining directly the properties of hot nuclear matter

27. SUMMARISING THE SIMPLE IDEA OF "PARTICLE THRESHOLD" • All residual products (yields) from any reaction which passed through at least one evaporation step show an even-odd staggering • The even-odd effect is complex even qualitatively • The complex behavior of the even-odd staggering can be reproduced qualitatively by the lowest separation energy (threshold energy) but not by the binding 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. Consequences of this simple idea... 1. consequence: a statistical evaporation code with correct ingredients (masses, level densities, competition of all possible channels –gamma emission-) should be able to reproduce the even-odd staggering 2. consequence: all other even-odd observables (e.g. Z distributions) do not contain any additional information and can be explained by the "fishbone pattern" (example: odd-even Z isospin anomaly)

28. A complete statistical evaporation code: ABRABLA07

29. A complete statistical evaporation code: ABRABLA07

30. 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

31. 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 ,

32. 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....

33. 1st aspect: memory effect 136,124Xe + Pb at 1 A GeV The isotopic distributions are systematically shifted

34. 2nd aspect: even-odd staggering min(Sn, Sp) min(Sn, Sp) Z=12 Z=13 The strength of the staggering is stronger along even-Z chains

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

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

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

38. CONCLUSIONS The measurements of cross-sections of all nuclides (A,Z) in the entire production range made at FRS, GSI, offered the possibility for the 1st time to observe and systematically investigate the complexity of the even-odd effect in the yields (Structural properties survive at low energies ) In nuclei which are the final products of an evaporation process, the even-odd structure is restored in the lastevaporation step It is not the binding energy 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 a pure Boltzmann approach when determining directly (neglecting evaporation) the properties of hot nuclear matter A statistical model can reproduce (in principle) the complexity of the even-odd effect. More complex effects (eg. anomaly) are in reality just a consequence of the observed characteristics of the even-odd effect in the individual yields.

39. Additional transparencies

40. MACROSCOPIC STATISTICAL DEEXCITATION MODEL + THRSHOLD METHOD • 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

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

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

43. 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 • indications that the pre-fragment distribution in the last evaporation step is not smooth • influence of unstable states • influence of the fluid-superfluid phase transition (some additional E* is gained from the formation of pairs)

44. ● N=Z■ N=Z+2 ▲N=Z+4 N=Z+6 ● N=Z+1■ N=Z+3▲ N=Z+5