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

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

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

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

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

FOLLOWING THE FOOTPRINTS OF THE DATA... Staggering in binding energy (MeV) (BE exp from Audi Wapstra – BE calc from pure LDM Myers, Swiatecky) Production cross sections (mb) for 56 Fe on Ti at 1 A GeV N=Z 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

FOLLOWING THE FOOTPRINTS OF THE DATA... Staggering in binding energy (MeV) (BE exp from Audi Wapstra – BE calc from pure LDM Myers, Swiatecky) Production cross sections (mb) for 56 Fe on Ti at 1 A GeV N=ZN=Z+1 ? 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

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

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)

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

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

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

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

STAGGERING IN YIELDS VERSUS min(Sn,Sp) Production cross sections 56 Fe+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! N=Z+1 cross sections particle threshold binding energies N=Z

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) Now we want to apply this simple idea...

1 st 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* < 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

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

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

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

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 (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)

TRUE ABRABLA07

2 nd APPLICATION: THE ODD-EVEN Z ISOSPIN ANOMALY L. B. Yang et al., PRC 60 (1999) 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:

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) Kr+ 12 C  90 Mo, 82 Kr+ 12 C  94 Mo T.S. Fan et al., NPA 679 (2000) Ni+ 12 C  70 Se, 64 Ni+ 12 C  76 Se Jean-Pierre Wieleczko, GANIL, 78,82 Kr + 40 Ca at 5.5 MeV, this conference MSU? Texas? 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)

OBSERVED AT FRS EXPERIMENTS, GSI 124 Xe 136 Xe D. Henzlova et al., PRC 78, (2008) ,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....

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

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

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!

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

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

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

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

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

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)