M. Valentina Ricciardi GSI, Darmstadt ORIGIN OF THE EVEN-ODD EFFECT IN THE YIELDS FROM HIGH-ENERGY REACTIONS Its role in the study of the properties of hot nuclear matter

Temperature: a very important variable Multifragmentation  establishing the caloric curve Yield ~ e -E/T Assumption: thermodynamic equilibrium Heat bath at temperature T T can be deduced from measured yields 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 N=Z even-odd effect N=Z+1 odd-even effect

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

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

o.o. o.e. o.e. /e.o. o.o. /e.e e.e. e.o. Understanding the staggering in the yields Sequential evaporation plays a decisive role Last step in the evaporation cascade

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

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

Conclusions It is not the binding energy (pure Boltzmann approach) that is responsible for the staggering in the yields but the separation energy Even the yields of the lightest multifragmentation products (e.g. Li) are governed by evaporation Warning to all methods based on Boltzmann statistics when determining directly the properties of hot nuclear matter Quantitative influence of even-odd effect in deducing the properties of hot nuclear matter Outlook