proximity splitting/breakup in mehir ( frustrated massive transfer ?)

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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W. Udo Schröder IWNDT 2013

1

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

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

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

pera

ture

(MeV

)

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

tion

Plan

e

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!)

proximity splitting/breakup in mehir ( frustrated massive transfer ?)

Documents

udo schrder iwndt

nucleusnucleus interactions

nuclear breakup

ny proximity splittingw

nuclear dynamics

tensile testing

residual interactions

bulk mean field eos