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

Temperature: a very important variable 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) 56Fe on Ti at 1000 A MeV FRS, GSI, Darmstadt, Germany P. Napolitani et al., Phys. Rev. C 70 (2004) 054607 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

Complex even-odd effect in the yields 56Fe on Ti at 1000 A MeV P. Napolitani et al., Phys. Rev. C 70 (2004) 054607 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 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 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)

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 0 ½ 0 ½ 0 ½ 0 ½ 0 ½ ½ 1 ½ 1 ½ 1 ½ 2 ½ 1 ½ 1 ½ 1 ½ 2 ½ 1 ½ 1 ½ 1 ½ 2 ½ 1 ½ 1 ½ 1 ½ 2 ½ 1 ½ 1 ½ 1 ½ 1 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

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

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

Staggering in yields vs. min(Sn,Sp) N=Z N=Z+1 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!

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 Outlook Quantitative influence of even-odd effect in deducing the properties of hot nuclear matter