m. valentina ricciardi gsi, darmstadt
DESCRIPTION
THE ROLE OF NUCLEAR-STRUCTURE EFFECTS IN THE STUDY OF THE PROPERTIES OF HOT NUCLEAR MATTER. M. Valentina Ricciardi GSI, Darmstadt. PROPERTIES OF HOT NUCLEAR MATTER. Multifragmentation establishing the caloric curve. Heat bath at temperature T. - PowerPoint PPT PresentationTRANSCRIPT
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.
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ground state
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ground state
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ground state
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ground state
ground state
ground state
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o.o. o.e. o.e. /e.o. o.o. /e.e e.e. e.o. o.o. o.e. e.e. e.o.
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ground state
ground state
ground state
daughter mother daughter mother
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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)