Clusters & LGPT M_2006 W. Udo Schröder 1 Cluster emission in intermediate-energy nuclear reactions and the nuclear “liquid-gas phase transition” Basic goal: Quantal A body system Lack of knowledge & understanding Beyond the mean field, correlations Nuclear stability at extremes (A, Z, E*, I) Nuclear thermodynamics/transport Isospin (asymmetry) effects Role of the diffuse nuclear surface Accessibility in (peripheral) heavy-ion collisions at intermediate energies, (perhaps also in fusion) Illustration of the disintegration of 197 Au after annihilation of an antiproton (impact from right). Snapshot of a hydro-dynamical calculation. [Nix80] W. Udo Schröder, Departments of Chemistry and Physics, University of Rochester, Rochester, NY 14627 USA J. Tõke, W. Gawlikowicz, J. Lu, WUS (Rochester) R.G. Charity, L.G. Sobotka, (St. Louis) R.T. deSouza (Bloomington)
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Clu
ster
s &
LG
PT
M_2006 W. Udo Schröder
1
Cluster emission in intermediate-energy nuclear reactions and the nuclear “liquid-gas phase transition”
Basic goal: Quantal A body system
Lack of knowledge & understanding
Beyond the mean field, correlationsNuclear stability at extremes (A, Z, E*, I) Nuclear thermodynamics/transportIsospin (asymmetry) effectsRole of the diffuse nuclear surface
Accessibility in (peripheral) heavy-ion collisions at intermediate energies, (perhaps also in fusion)
Illustration of the disintegration of 197Au after annihilation of an antiproton (impact from right). Snapshot of a hydro-dynamical calculation. [Nix80]
W. Udo Schröder, Departments of Chemistry and Physics, University of Rochester,
Rochester, NY 14627 USA
J. Tõke, W. Gawlikowicz, J. Lu, WUS (Rochester) R.G. Charity, L.G. Sobotka, (St. Louis) R.T. deSouza (Bloomington)
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M_2006 W. Udo Schröder
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Outline
• Introduction: Intermediate energy HI reaction domain How to map nuclear phase diagram (?)
• Experiment: Cluster emission in the dissipative reaction environment
• Models: ConventionalExpansion and surface phenomena, stability and decay of hot nuclei
• Conclusions
Clu
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M_2006 W. Udo Schröder
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Macroscopic clusters: Surface ablation with lasers
(Zhigelej et al., 2000)
Goals: Mechanism (thermodynamical, dynamical), dependence of cluster multiplicities & sizes on energy
surface physics, nano materials
Low energy
High energy
Low energy: few large clustersHigh energy: many small clusters vaporization
Equilibrium molecular dynamics models
Reaction Scenarios
Clu
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M_2006 W. Udo Schröder
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Near the Barrier(E/A =5-20 MeV)
Projectile
Target
Projectile-like fragment
Target-like fragment
Dissipative Collisions leading to Focussing and Orbiting
Dotted: average ridge lines for E/A=28, 40, 62 MeV.
E*, bIndependent of ELab
Also (SB): P(TKEn), 5 ∆Θ
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Unusual Statistical Features of Cluster Emission
E*
E*
E*
E* E*
E* E*
inclusive
E* E* Regions in mn/mlcpplane correspond to regions in total excitation energy E*of reaction fragments
For mIMF = 3,4…,8 no change in illuminated E* region.
Challenge: statistical competition clusters and light particles?Valid for all cluster components???
spontaneous multi-fragmentation?
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Detector Response to Charged Particles
TLF
PLF
PLF+TLF
Average cluster emission patterns (Zcluster > 2, deduce A from A≈Aattractor)
Energy resolution, angular resolution (granularity), detection/ID thresholds all distort the ideal (circular) kinematical pattern
Beam Direction
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Light Charged Particles and Clusters
Sources are kinematically correlated with PLF (projectile-like fragment)TLF (target-like fragment)IVS (Intermediate velocity source = “CN”, pre-equilibrium)
Similar invariant velocity distributions for LCP & IMF clusters (3 ≤ Z≤10)
Concentrate first on sequential cluster emission from PLF (well prepared)
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Moving-Source Parameterization of Cluster Emission
Semi-peripheral Central
“b“ Selection: P(mn , mlcp)
Cluster multiplicities increase with decreasing b, increasing mIVS/(mPLF+mTLF). IVS clusters have much harder (“PE” type) spectra than PLF clusters.
Clu
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Outline
• Introduction: Intermediate energy HI reaction domain How to map nuclear phase diagram (?)
• Experiment: Cluster emission in the dissipative reaction environment
• Models: ConventionalExpansion and surface phenomena, stability and decay of hot nuclei
• Conclusions
Clu
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M_2006 W. Udo Schröder
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Challenges to Conventional Statistical Models
Fundamental problems for stat. cluster emission (mcluster > 1):
• high emission barriers: VB ≈ (50-60) MeV, T [ 5-6 MeV• nuclear interactions non negligible even at ρ < ρ0/3.
Shortcomings of conventional statistical models
No, or unrealistic, reaction scenarios
EESM: “scales” the barrier at the expense of compressional, and not thermal energy.
SMM, MMMC: “scale” the barrier one nucleon at time – rely on randomized gas flux (perfectly reflecting container walls).limited account of entropy (neglect of ρ < ρ0 , level density)
Fisher’s droplet model: does not treat emission. Questionable adaptations
Percolation: does not treat emission.
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Surface Matter/State Density
Number (i a ) of states/nucleon is larger in the diffuse surface than in the dense bulk.Tõke & Swiatecki NPA 372, 141(1981)
bulk
surface
Nuclear Matter Distribution
r (fm)
ρ C(r
) (1
01
9C
/cm
3)
Light nuclear clusters (e.g., 12C) are mostly surface
( ) 2 ( ) * ( , *) /, * a A E S A E kA E e e⋅Ω = =Fermi gas density of states
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o
ρρ
/ oρ ρ
Thermal Expansion: Equilibrium Density
( )
*
*
*
2
1 (1 9 8 )4
0
ρ
ρ
ρ
∂ ∂ =
= ⋅
→
= + −
therm
eq Total
o Bin
E
ding
S a E
E
S
E
0
2 323( ) ( )ρ ρα α −
= +
= +
SurVolume
V
ace
S o
f
a
Level Density Paramete
A
ra a
A
a
Density drops to ρ0/3 before disassembly nucleons
2bind
* 2 / 3 2therm 0
*c r 0omp
*0E E aE ( ) T1 )E ( ρ ρ ρρ −− ⋅= + = +
EOS-harmonic approximation
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Effects of Irreversible Nuclear Expansion
Caloric Curve
(Effects of m*) Sobotka PRL 2004
Weisskopf, ρ0
HIFG, ρequ
T non monotonic, plateau
Evaporation time
Softening/melting of surface reduction in energy of surface normal modes stability loss.
Reduction of T increased evaporation time increased stability/lifetime
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Multipole Surface Vibrations as MF Doorways ?
22 3
1 3
5 ( 1)( 1)( 2)
4 2 (2 1)s
cb Z
C AAλ
λλ λπ π λ
−= − + −
−b Bohr & Mottelson II, Ch. 6
actually an over-estimate !
5 42 2
2 2
24
&
( ) 17.5
( ) 0.7 1 7.6 10
cs
c
C
Shlomo Kolomietz
T Tb T MeV
T T
Tb T MeV
MeV−
⎛ ⎞−= ⋅ ⎜ ⎟⎜ ⎟+⎝ ⎠
⎛ ⎞⎛ ⎞= ⋅ − ⋅⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
With increasing E* decreasing γdecreasing energy of λ modeπdegeneracy of different λdevelop at same E*(mn, mlcp)
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Cluster Decay of Excited Nuclei
saddle config
mon
on
ucle
us
Entropy per nucleon for
• Mono-nucleus: 208Pb* parent• Dinucleus: 192W residue in nuclear contact with 16O cluster
True saddle-point
Vnucl
VCoul
VTotal
(fm)
dinucleus
Effective Emission BarriersClu
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BEffS TP e e
−∆∝ = EffB T S= − ∆ ,∆ = −Saddle diN monoNS S S
EffB(MeV)
T (MeV)
Without surface effects
With surface effects
Dramatic entropy gains at high T favor cluster emission
197Au
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Fragment Emission Probabilities
ClusterZ
Cluster
p
pp
For E*/A > 5 MeV 16O emission from 197Au more likely than proton emission !
mIMF>1 because Q<0 for heavy CN*
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Academic Considerations: Boxed Fermi Matter
If one could confine nuclear matter (A, Z) in a box with perfectly reflecting walls (V = Vliqu+Vgas = const., T= const.) equilibration to maximum entropy minimum of free energy F
ρ ρ ρ ρ −
= + −
= − = − −
= − ⋅
⋅
* * 2compr therm
* 2 2 2 / 3 2compr bind 0
*t
0 0
otal E E 2aT
E aT E (1 ) a ( )
F T S
T
E
2 2 3
20
0 0
1ερ ρ
−⎛ ⎞ ⎛ ⎞
= − −⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
gas gasgas gas Bind gas
gas gas
A AF A A a T
V V
2 2 3
20
0 0
1ερ ρ
−⎛ ⎞ ⎛ ⎞
= − −⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
liqu liquliqu liqu Bind liqu
liqu liqu
A AF A A a T
V V
Isotherms of Nuclear MatterIsotherms of Confined Nuclear Fermi MatterClu
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Real gas of interacting nucleons in confined volume V, T-const.
Spinodal
Compression leads to liquefaction. Results automatically from minimization of
F=Fliqu+Fgas
Maxwell construction not necessary.
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Liquid-Gas Coexistence Line of Fermi Matter
/ρ ρo
T( )MeV
Critical exponent α=0.5 for ρ(T-Tc)
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Conclusions: Dynamics & Thermodynamics of Cluster Decay
• There are different modes of cluster emission: non-equilibrium and equilibrium
• Found that expansion of hot nuclear matter changes high-T statistical decay pattern significantly ∆S, ∆Ssurf
• Entropy-driven decay favors clusters over simple particles, surface melting equivalent to phase transition
• Exact mechanism of cluster formation and decay not yet determined.
• If one can establish mechanism, then new access to (isospin) nuclear EOS.
• New important study of nuclear surface becomes possible