M. Valentina RicciardiGSI, Darmstadt

THE ROLE OF NUCLEAR-STRUCTURE EFFECTS THE ROLE OF NUCLEAR-STRUCTURE EFFECTS IN THE STUDY OF THE PROPERTIES IN THE STUDY OF THE PROPERTIES

OF HOT NUCLEAR MATTEROF HOT NUCLEAR MATTER

PROPERTIES OF HOT NUCLEAR MATTERPROPERTIES OF HOT NUCLEAR MATTER

Multifragmentation establishing the caloric curve

Heat bath at temperature T

T can be deduced from measured

yields

Yield ~ e-E/TAssumption: thermodynamic equilibrium

light fragments

investigated

MOVING TOWARDS HEAVIER FRAGMENTS MOVING TOWARDS HEAVIER FRAGMENTS

Very precise production cross-sections on the entire production range (from high-resolution magnetic spectrometers)

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

56Fe on Ti at 1000 A MeV FRS, GSI, Darmstadt, Germany

P. Napolitani et al., Phys. Rev. C 70 (2004) 054607

COMPLEX EVEN-ODD EFFECT IN THE YIELDS 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

binary

decay

excluded!

FOLLOWING THE FOOTPRINTS OF THE DATA... 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... FOLLOWING THE FOOTPRINTS OF THE DATA...

Staggering in binding energy (MeV) (BEexp from Audi Wapstra – BEcalc from pure LDM Myers, Swiatecky)

Production cross sections (mb) for 56Fe 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... FOLLOWING THE FOOTPRINTS OF THE DATA...

Staggering in binding energy (MeV) (BEexp from Audi Wapstra – BEcalc from pure LDM Myers, Swiatecky)

Production cross sections (mb) for 56Fe on Ti at 1 A GeV

N=Z N=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 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 10 ½ 0 ½ 0 ½ 0 ½ 0 ½ ½ 1 ½ 1 ½ 2 ½ 1 ½ 10 ½ 0 ½ 0 ½ 0 ½ 0 ½ ½ 1 ½ 2 ½ 1 ½ 1 ½ 10 ½ 0 ½ 0 ½ 0 ½ 0 ½ ½ 2 ½ 1 ½ 1 ½ 1 ½ 10 ½ 0 ½ 0 ½ 0 ½ 0 ½ e o e o e o e o e o

oddZNfor2

oddoddfor1

evenoddfor2

1evenevenfor0

withAA

ZN

2

3

o

e

o

e o

e o

e

N=Z+1N=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 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. e.e. e.o.

Svmother

Svmother

ground state

ground state

ground state

ground state

daughter mother daughter mother

Svdaughter Sv

daughter

Sv

2

o.o. o.e. e.e. e.o.

Svmother

Svmother

ground state

ground state

ground state

ground state

daughter mother daughter mother

Svdaughter Sv

daughter

Sv

2

o.o. o.e. e.e. e.o.

Svmother

Svmother

ground state

ground state

ground state

ground state

daughter mother daughter mother

Svdaughter Sv

daughter

Sv

2

o.o. o.e. e.e. e.o.

Svmother

Svmother

ground state

ground state

ground state

ground state

daughter mother daughter mother

Svdaughter Sv

daughter

Sv

2

o.o. o.e. o.e. /e.o. o.o. /e.e e.e. e.o. o.o. o.e. e.e. e.o.

Svmother

Svmother

ground state

ground state

ground state

ground state

daughter mother daughter mother

Svdaughter Sv

daughter

Sv

2

o.o. o.e. e.e. e.o.

Svmother

Svmother

ground state

ground state

ground state

ground state

daughter mother daughter mother

Svdaughter Sv

daughter

Sv

2

UNDERSTANDING THE STAGGERING IN THE YIELDS UNDERSTANDING THE STAGGERING IN THE YIELDS

Last step in the evaporation cascade

THE KEY ROLE OF THE SEPARATION ENERGY THE KEY ROLE OF THE SEPARATION ENERGY

"Energy range" = min(Sn, Sp) keV

data from Audi-Wapstra

THE KEY ROLE OF THE SEPARATION ENERGY THE KEY ROLE OF THE SEPARATION ENERGY

data from Audi-Wapstra

THE KEY ROLE OF THE SEPARATION ENERGY THE KEY ROLE OF THE SEPARATION ENERGY

data from Audi-Wapstra

Sequential evaporation plays a decisive role

STAGGERING IN YIELDS VERSUS min(Sn,Sp)STAGGERING IN YIELDS VERSUS min(Sn,Sp)

Production cross sections 56Fe+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 cross sectionsparticle threshold

particle threshold

binding energiesbinding energies

N=Z

SUMMARISING THIS SIMPLE IDEASUMMARISING 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) 2199.

Now we want to apply this simple idea...

11stst APPLICATION: THIS IDEA IN A STATISTICAL DEEXCITATION MODEL 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* < 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

COMPLEX EVEN-ODD EFFECT IN THE YIELDS COMPLEX EVEN-ODD EFFECT IN THE YIELDS

56Fe on Ti at 1000 A MeV P. Napolitani et al., Phys. Rev. C 70 (2004) 054607

RESULTS: RESULTS: 5656Fe on Ti at 1000 A MeVFe on Ti at 1000 A MeV

Experiment ABRABLA07 (LDM) + Threshold method

RESULTS: RESULTS: 5656Fe on Ti at 1000 A MeVFe on Ti at 1000 A MeV

Experiment ABRABLA07 (LDM) + Threshold method

5656Fe on Ti at 1000 A MeVFe on Ti at 1000 A MeV

Comparison experiment vs. ABRABLA07 (LDM) + Threshold method

Qualitatively: good result n and p evaporation are dominantQuantitatively: 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 ABRABLA07TRUE ABRABLA07

TRUE ABRABLA07TRUE ABRABLA07

22ndnd APPLICATION: THE ODD-EVEN Z ISOSPIN ANOMALY APPLICATION: THE ODD-EVEN Z ISOSPIN ANOMALY

L. B. Yang et al., PRC 60 (1999) 041602

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 SYSTEMSOBSERVED IN MANY OTHER SYSTEMS

E. Geraci et al. NPA 732 (2004) 173

Y(112Sn + 58Ni)Y(124Sn + 64Ni)

at 35 A MeV

K.X.Jing et al., NPA 645 (1999) 203 78Kr+12C90Mo, 82Kr+12C94Mo

T.S. Fan et al., NPA 679 (2000) 121 58Ni+12C70Se, 64Ni+12C76Se

Jean-Pierre Wieleczko, GANIL, 78,82Kr +40Ca at 5.5 MeV , this conference

MSU? Texas?

40Ca158Ni/40Ca158Fe 40Ar158Ni/40Ar158Fe 25 MeV/nucleon

Winchester et al., PRC 63 (2000) 014601

OBSERVED AT FRS EXPERIMENTS, GSIOBSERVED AT FRS EXPERIMENTS, GSI

124Xe 136Xe

D. Henzlova et al., PRC 78, (2008) 044616

136,124Xe + 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....

11stst ASPECT: MEMORY EFFECT ASPECT: MEMORY EFFECT

136,124Xe + Pb at 1 A GeV

The isotopic distributions are systematically shifted

22ndnd ASPECT: EVEN-ODD STAGGERING ASPECT: EVEN-ODD STAGGERING

keVmin(Sn, Sp)

The strength of the staggering is stronger along even-Z chains

Z=12

Z=13

min(Sn, Sp)

A MATHEMATICAL GAMEA 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: RESULTS: 136,124136,124Xe on Pb at 1000 A MeVXe on Pb at 1000 A MeV

RESULTS: RESULTS: 5858Ni+Ni+5858Ni / Ni / 5858Fe+Fe+5858Fe at 75 A MeV Fe at 75 A MeV

CONCLUSIONSCONCLUSIONS

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

33rdrd APPLICATION: ODD-EVEN STAGGERING IN THE <N>/Z OF APPLICATION: ODD-EVEN STAGGERING IN THE <N>/Z OF FRAGMENTSFRAGMENTS

W. Trautmann, NPA 787 (2007) 575c D. Henzlova et al., PRC 78, (2008) 044616

The odd-even in <N>/Z effect is stronger for neutron-poor systems

33rdrd APPLICATION: ODD-EVEN STAGGERING IN THE <N>/Z OF APPLICATION: ODD-EVEN STAGGERING IN THE <N>/Z OF FRAGMENTSFRAGMENTS

The odd-even in <N>/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)