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 Without pairing With pairing Even-odd

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

5. 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 liquid coexistence gas E * /MeV 5 7010300 A  25 0.5 T/MeV 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. EVEN-ODD STRUCTURE IN LOW-ENERGY FISSION 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) SUPERFLUIDITY Z fiss =90Z fiss =89

7. de-excitation by fission / evaporation cold fragment superfluid compound nucleus collision E.g.: transfer abrasion 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. Knott et al., Phys. Rev. C 53 (1996) 347 40 Ca + p Ch. O. Bacri et al., Nucl. Phys. A 555 (1998) 477 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/Z from time and position: Z from IC: Experimental set-up at the FRagment Separator (FRS), GSI 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

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

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

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. Can we explain this complex behavior? evaporation cold fragment with structure compound nucleus collision E.g.: transfer abrasion without structure We have this picture in mind: 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 E critical (~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. o.o. o.e. o.e. /e.o. o.o. /e.e e.e. e.o. Understanding the staggering in the yields Last step in the evaporation cascade (assuming only n and p evaporation) The lowest particle separation energy is the key quantity!

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

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

18. Conclusions concerning the yields from nuclei in the 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 Yield ~ e -Ei/kT Heat bath at temperature T light fragments investigated 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 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 ). the ground state has highest probability to be populated

21. Even-odd effect in the yields of multifragmentation products 56 Fe 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 N=Z Staggering in binding energy (MeV) (BE exp from Audi Wapstra – BE calc from pure LDM Myers, Swiatecky) N=Z+1 ? Production cross sections (mb) 56 Fe on Ti at 1 A GeV cross sections binding energies cross sections

23. Overview on the staggering in the binding energy 0 ½ 0 ½ 0 ½ 0 ½ 0 ½ ½ 1 ½ 1 ½ 1 ½ 2 ½ 1 0 ½ 0 ½ 0 ½ 0 ½ 0 ½ ½ 1 ½ 1 ½ 2 ½ 1 ½ 1 0 ½ 0 ½ 0 ½ 0 ½ 0 ½ ½ 1 ½ 2 ½ 1 ½ 1 ½ 1 0 ½ 0 ½ 0 ½ 0 ½ 0 ½ ½ 2 ½ 1 ½ 1 ½ 1 ½ 1 0 ½ 0 ½ 0 ½ 0 ½ 0 ½ Extra binding energy associated with the presence of congruent pairs: most bound less bound staggering in the ground-state energies (Myers Swiatecki NPA 601, 1996, 141) N=Z N=Z+1 e o e o e o e o e o eoeoeoeoeoeoeoeo It is not the binding energy responsible for the staggering in the cross sections

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) 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! N=Z N=Z+1 cross sections particle threshold binding energies

26. Conclusions concerning the yields from nuclei in the Conclusions concerning the yields from nuclei in the COEXISTENCE 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

30. The odd-even Z isospin anomaly N/Z = 1.07 N/Z = 1.23 Elemental even-odd effect decreases with increasing neutron-richness of the system. This fact is also reflected in this figure: L. B. Yang et al., PRC 60 (1999) 041602

31. Observed in many other systems E. Geraci et al. NPA 732 (2004) 173 Y( 112 Sn + 58 Ni) Y( 124 Sn + 64 Ni) at 35 A MeV K.X.Jing et al., NPA 645 (1999) 203 78 Kr+ 12 C  90 Mo, 82 Kr+ 12 C  94 Mo T.S. Fan et al., NPA 679 (2000) 121 58 Ni+ 12 C  70 Se, 64 Ni+ 12 C  76 Se Jean-Pierre Wieleczko, GANIL, 78,82 Kr + 40 Ca at 5.5 MeV, 40 Ca 158 Ni/ 40 Ca 158 Fe 40 Ar 158 Ni/ 40 Ar 158 Fe 25 MeV/nucleon Winchester et al., PRC 63 (2000) 014601

32. Observed at FRS experiments, GSI 124 Xe 136 Xe D. Henzlova et al., PRC 78, (2008) 044616 136,124 Xe + Pb at 1 A GeV 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. 1 st aspect: memory effect 136,124 Xe + Pb at 1 A GeV The isotopic distributions are systematically shifted

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

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

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

37. RESULTS: 58 Ni+ 58 Ni / 58 Fe+ 58 Fe 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 1 st 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 last evaporation 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* < E last ) we stop the statistical treatment We treat the last evaporation step with the "threshold method" (deterministic) THRESHOLD METHOD (E* < E last ) Pre-fragment: N,Z Final fragment If E* lower than Sn, Sp+B p 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: 56 Fe on Ti at 1000 A MeV ExperimentABRABLA07 (LDM) + Threshold method

42. RESULTS: 56 Fe on Ti at 1000 A MeV ExperimentABRABLA07 (LDM) + Threshold method

43. 56 Fe 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 Enhanced production of even-Z nuclei Staggering of same strength (~10%) for N=Z+2, N=Z+4, N=Z+6 chains Staggering particularly strong (~50%) for the N=Z chain Staggering gradually disappears as Z increases Enhanced production of odd-Z nuclei The strength of the staggering increases for n-rich chains In the N=Z+1 chain the staggering turns from odd-even to even-odd as Z increases Staggering gradually disappears as Z increases