Proximity Splitting/Breakup in MEHIR ( Frustrated Massive Transfer ?)
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Proximity Spl i t t ing/Breakup in MEHIR(Fr u s t r a t e d M a s s i v e Tr a n s f e r ? )
W. Udo SchröderUniversity of Rochester, Rochester, NY
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International Workshop on Nuclear Dynamics and Thermodynamics
Honoring Joseph B. (“Joe”) Natowitz
College Station (TX), August 2013
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2 Outline:Challenges Mechanical (in)stability, tensile strengthSimple expectationsExpt example: 48Ca+112,124Sn @45A MeVConclusions
M.J. Quinlan, H. Singh, E. Henry, J. Tõke, WUS and CECIL/CHIMERA Collaboration (Univ. Rochester, LNS/Catania,…)
48Ca+124Sn Reaction. E/A=45 MeV, b= 5 fm, QMD simulation, soft EOS M.J. Quinlan, PhD Thesis, U. Rochester, 2011
Influence of mean field vs. residual interactions (scattering) EOS/isoEOS compatible with interactions/decay of finite nucleiMethod: Statistical vs. dynamical particle emission (h, E*/T/r ).
Basic Questions and Challenges in HIR Dynamics
Challenges to Studies of “the” EOS/isoEOS • Preparation (A, Z, E*, J) of highly excited,
equilibrated systems at limits of stability.
• Understanding of EOS-driven expansion and decay mechanism of finite nuclei.
• Interest in bulk mean field (EOS), …. But exotic clusters (=instability) evaporated from surface.
• Competing reaction mechanisms produce similar phenomena (e.g. isotopic distributions), fission, neck rupture, but different sensitivity/response.
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Q: Are there additional useful processes, observables? dynamical processes: aligned dynamical fission/breakup proximity splitting ( a number of recent works, here example Ca+Sn).
• Superposition of effects of mean field with those of residual interactions (in-medium scattering, “pre-equilibrium”).
• Secondary evaporation effects/”side feeding.”
What can be learnt from dyn. fission/breakup
EOS and Tensile StrengthP
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F=LoadForce required for nuclear breakup depends on T, A/Z and on transitional nuclear shapes (light vs. heavy nuclei). Available forces: centrifugal, nucleus-nucleus interactions, thermal pressure.
J. R. Davis, Tensile Testing, ASM Intern., 2004
Fracture
Ductile Metal
2 3 5 3
00 0
20
2
03 5
( ) ( )
??
:
, ; :
:
)!
:
(
0
F
kin
I
Mean field bulk equation of state example
E A E A a b
ISurface Not well kno
c I I N Z A
Internal pressure bulk not surface propert
P
ny
w
r r r rr
rr
r r
r r
minint
" "( . . )
2
Minimum
neckexternal
Tensile StrengthG F Bertsch
LoadInstability for P P rArea
EOS and Tensile StrengthP
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2 3 5 3
00 0
20
2
03 5
( ) ( )
??
:
, ; :
:
)!
:
(
0
F
kin
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Mean field bulk equation of state example
E A E A a b
ISurface Not well kno
c I I N Z A
Internal pressure bulk not surface propert
P
ny
w
r r r rr
rr
r r
r r
minint
" "( . . )
2
Minimum
neckexternal
Tensile StrengthG F Bertsch
LoadInstability for P P rArea
J. R. Davis, Tensile Testing, ASM Intern., 2004
Fracture
Ductile Metal
Centrifugal-Force Effect
30.7 MeV fm
F=LoadForce required for nuclear breakup depends on T, A/Z and on transitional nuclear shapes (light vs. heavy nuclei). Available forces: centrifugal, nucleus-nucleus interactions, thermal pressure.
Dynamical (Centrifugal) Instabilities
Stability criteria for dynamical system, state= {density profile r(r), shape par’s, E*,J}
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Spherical Triaxial Binary
Estimate trends: RLDM at T≠0, Scale Esurf with
(Erot(J)/Esurf)crit = f(T)
But: No expansion d.o.f. !!
Rotating-liquid drop model (g.s.) (Cohen, Plasil, Swiatecki, Ann. Phys. 82 (1974))Instability = f (shape, J), specific families of nuclear shapes. * 0intrE
0 0
,
: 0 0( ) : 0
,det 0
, Re 0
i i j j
i i i
i i
i i
Equations of Motion x f m x
Equilibrium state x f x
Stability Lyapunov x xMatrix f x positive definite
EV equationcomplex eigen values stable
AA
A I
0 1 5T T MeV
48Ca
rot
surf crit
EE
Angular Momentum J
Expectations for Peripheral Ca+Sn CollisionsP
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Angular Momentum (h)
Tem
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ture
(MeV
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Classical transport model (NEM) calculations.
Proximity +Coulomb interactions, one-body dissipation.
Ca+Sn 45 A MeV typical ranges
22(1 2) 10(200 600)(4 6)(10 30)
int
diss
PLF
PLF
t sE MeVT MeVJ
Interaction Time (L)
PLF Temperature (L)
PLF Mean Spin (L)
Dissipated Energy (L)
Can projectile (PLF) sustain E*,J ?
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8Experiment: 48Ca + 112,124Sn @ 45 A MeV
Cone
1m
1°
30°
CHIMERA Multi-Detector Array (LNS Catania)
TARGET
BEAMCone: 688 telescopes
Sphere
40,48Ca+112,124Sn Reaction. E/A=45 MeVM.J. Quinlan, PhD Thesis, U. Rochester, 2011
No neutrons
48Ca + 112,124Sn @ 45 A MeVP
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E(Si)-E(CsI) correlations for different elements for 48Ca + 124Sn at laboratory angle θ = 19o.
Angle-integrated isotopic distributions for both targets are approximate Gaussians with similar widths.Heavier target n rich PLF
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Dynamic Splitting of PLF* after Dissipative Rxns48Ca+112,124Sn, E/A = 45 MeVExperimental Wilczyński contour diagrams for 48Ca+112Sn @E/A=45 MeV. Top: PLF energy vs. angle, Bottom: PLF velocity vs. angle. Nucleon exchange model (CLAT). Sequential evaporation: GEMINI.
Galilei invariant cross sectionsa) for heavier PLF remnants
b) for lighter remnants (IMFs).
Wilczyński Plots
Invariant Velocity Plots
Proximity Splitting of PLF* after Dissipative RxnsP
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Prompt projectile splitting in proximity (under the influence) of target. Nuclear surface interactions aligned asymmetric breakup
Evidence for dynamics:1. Alignment of breakup axis
in plane, in direction of flight2. F/B of heavy/light. 3. Relative velocity ≈2x systematics.4. Anti-correlation Z: Z1 + Z2≈ ZPLF*
48Ca+112,124Sn
Reac
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Plan
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Angular Alignment and CoplanarityP
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Statistical x 4
Angular Distribution of light IMF clusters
Qtilt (deg.)
Distribution of Tilt Angles (of Split-Axis)
Orientation of the PLF scission axis QTilt≈ 900±250. Coplanarity
Preferred orientation of deformed pre-scission PLF: lighter IMF backwards (towards TLF) Minimizing energy/L
Relative IMF/PLFrem velocity
48Ca + 124Sn E/A =45 MeV Multiplicity Correlations
Projectile velocity v||= 9 cm/ns
Multiplicity distributions indicate semi-peripheral (fast) reactions for
More central (smaller L) if IMF is emitted forward
Charged-Particle Multiplicity Distributions
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Relative IMF/PLFrem velocity
IMF/PLFrem Angle-Velocity CorrelationsP
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Experiment
SimulationNEM/GEMINI
SimulationQMD/GEMINI
vC = Viola Systematics
NEM & QMD simulations:Fragment emission is sequential (via GEMINI) or late in collision.
( 40, 20) 29
2 4rot
rel Coul rot red
E A J MeV
E E M cm ns
Centrifugal energy boost: Required J values are consistent with J stability limit for Ca.
But does not explain F/B alignment and yield asymmetry.
Centrifugal energy boost
vrel
TLF-(IMF+PLFrem) Int ?
3-Body Driving Potential (Proximity + Coulomb)P
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rP
rdef
L=0 L=80
L=160 L=300
B.R. Binary ReactionF. Complete FusionI.F. Incomplete FusionP.S. Projectile Splitting
3-Body Driving Potential (Proximity + Coulomb)P
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rP
rdef
L=0 L=80
L=160 L=300
B.R. Binary ReactionF. Complete FusionI.F. Incomplete FusionP.S. Projectile Splitting
Isoscaling in Dynamic PLF* Splitting (48Ca+112,124Sn)P
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48 1,
1 112
4
4,
2
2 8
( , )
: N Z
N Z
PLF PLF N Z
Y
Sn
aR
Y
SnC
Ca
PLFs from 2 dissipative reactions split dynamically. Compare cluster yields ratios.
Isoscaling Plot Li, Be, B, C, N Isotones
12nR N Z
R 12
2 21 2
2 21 2
4
4
sym CN CN
sym CN CN
T C Z A Z A
T C N A N A
Ambiguity due to uncertain reconstruction Isoscaling due to interaction of breakup fragments?Need reaction model to simulate simultaneous observables. Need realistic model to relate {, } Csym(r)
2 2 2
= ( )
2.6= ( ) 17( 0.3)
*1 1 1*
sym
PLF Z = 20, A = 49
PLF Z = 18, A = 43 C M VMeV
eT
2 2
5.5 0.3
= ( )
= ( ) 31( )
*1 1 1*
2 sym
PLF Z = 25, A = 48
PLF Z = 26, A = 49T M
C M VeV
e
Apparent
Apparent
?
Summary & ConclusionsExperimental observations (Ca+Sn, 45A MeV) • Reaction mechanism changes for semi-peripheral collisions from
binary (PLF+TLF) to PLF* splitting in TLF proximity.Estimates: JPLF~ (20-25)ħ, TPLF~ 5 MeV.Relative velocity augmented by centrifugal boost.
• Breakup instability suggests softening of surface, 0 for T (5-6) MeV• Breakup alignment indicates influence of underlying PES (TLF proximity).
• Potential of dynamical breakup processes to image bulk EOS, tensile strength. Process much faster than (collective) shape evolutions.
• Isoscaling observed also for competing mechanisms (dynamic splitting).• Ground state masses explain isoscaling phenomena.
• Progress in thermodynamics of finite nuclei (expansion, surface, caloric).• Theoretical work needed to derive more rigorous/direct connection
between EOS (hot RLDM?) and dynamic processes.
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Thank You!
(Joe, keep up the good work!)