1. NEW SIGNATURES ON DISSIPATION FROM THE STUDY OF
RELATIVISTIC HEAVY-ION COLLISIONS
Beatriz Jurado Apruzzese
August 2002

2. Contents Introduction and motivation
New experimental approach to investigate dissipation
Experimental set-up
Experimental observables sensitive to dissipation
Results
Conclusions

3. Introduction Deexcitation process of the nucleus: Statistical model
Dynamical model
Transport theories
Two types of degrees of freedom
Collective intrinsic
Dissipation:
 = dEcoll/dt [1/(Eeqcoll – Ecoll)]
 rules the relaxation of the coll. degrees of freedom
 (T, q)
Fission is an appropriate tool for investigating dissipation

4. Current knowledge on dissipation
Theory:
Hilscher et al.
Phys. Atom. Nucl. 57 (1994) 1187

5. Standard reaction mechanisms to induce fission
Experiment:
Standard reaction mechanisms to induce fission
Heavy-ion collisions at Eprojectile ≈ 5-10 A MeV
(Fusion-Fission, Fast fission, Quasifission)  ??
Dynamical models needed to describe these reactions
Antiproton annihilation and spallation reactions
...
Simplified theoretical description
Difficulty to reach very high E* with large cross sections

6. Standard experimental observablesU
Deformation (q)
fiss , evap
l-distrib. of evap. residues
Even-odd effect
TKE
Pre-scission part. and -multiplicities
Ang., mass and charge distrib.

7. Latest experimental results
Deformation dependence
Small deformation
Large &small deformation
[FrG93, fiss, evap, Mp]
[VeM99, A-, - distrib.]
[ShD00, M]
[DiS01, evap, M]
[HuS00, Dio01, l-distrib]
[JiP01, fiss]
[LoG01,Pfss]
[BeA02, fiss, 2z]
[ChP02, Pre-sadel, Mn]
[NaA02, Pfiss, fiss]
[SaF02,Pfiss]
Here you have to comment the possible reasons for controversy:
Fusion-Fission reactions require complicated theoretical tools that have to take into account the side effects
Often the excitation energy of the nucleus is too low
Additional observables are required that allow for selecting the excitation energy of the fissioning nucleus
Temperature dependence ??
Fissility dependence ??

8. Peripheral heavy-ion collisions at relativistic energies
Small shape distortion
Low angular momentum
High intrinsic excitation energies E* ~ ∆A
238U (1 AGeV) + Pb
(Calculation Abrasion
Model)
P (1.2 GeV) + U
(Experimental Data)
(Goldenbaum et al., Phys. Rev. Lett. 77 (1996 ) 1230)
Inverse kinematics

10. Experimental set-up for fission studies in inverse kinematics

11. Total fission cross sections
Observables
Total fission cross sections Y Z
Beam
Target IC
Fragmentation background
Fission events
Energy loss in IC
Double IC

12. New observables: Partial fission cross sections &
Widths of the charge distributions
Tfiss
Z1 + Z2 = 89
E*initial
z2 = Tfiss/Cz
Z1+Z2 = 92
238U (1 A GeV) + (CH2)n Bf
E*initial
Y fiss (Z1 + Z2)

13. M.V. Ricciardi PhD. Thesis
The model
Updated version of GSI code ABRABLA:
If T< 5.5 MeV
ABRASION
EVAPORATION / FISSION
af/an (Ignatyuk) Bf
(Sierk)
If T > 5.5 MeV
SIMULTANEOUS
BREAK-UP
Freeze out T = 5.5 MeV
M.V. Ricciardi PhD. Thesis

14. Model of Grangé & Weidenmüller (1980) Kramers (1940)
Numerical solution of the FPE under specific initial conditions
f(t) = f(t)/ħ
 = 51021s-1
T= 3 MeV
A = 248
Transient time f
f(t) =Num. Sol. FPE
(K.-H. Bhatt, et al., Phys. Rev. C 33 (1986) 954)
f(t) = Step Function
f(t) ∝(1-exp(-2.3t/f))
f(t) = Analytical approximation

15. Dependence of  on fiss(t)
fnucl 238U(1 A GeV) + Pb
Experiment
2.160.14 b
Transition-state model
3.33 b
f(t) step
 = 21021 s-1
2.00 b
f(t) ~1-exp(-t/)  = 41021 s-1
2.04 b
f(t) FPE
2.09 b
The value of  depends on the description for f(t)

16. Influence of  on f (Z1+Z2) and Z-Width(Z1+Z2)
238U (1 A GeV) + (CH2)n
Experimental data
Transition-state model
 = 2·1021s-1
 = 0.5·1021s-1
 = 5·1021s-1
 = 2·1021s-1
f  (1.7±0.4)10-21 s

17. Target dependence of ftot
238U (1 A GeV)
Experimental data
Transition-state model
 = 2·1021s-1
The minimum at Ztarget = 6 can only be reproduced if dissipation is included

18. For fission events produced 238U(1A GeV)+Pb
Calculations:
For fission events produced 238U(1A GeV)+Pb
NO BREAK-UP
BREAK-UP
Fission is mainly suppressed by dissipation at high E*
Fission completely suppressed at E*  350 MeV

19. Our result! [FrG93] [VeM99] [ShD00] [DiS01] [HuS00, Dio01] [JiP01]
[LoG01]
[BeA02]
[ChP02]
[NaA02]
Deformation dependence
Small deformation
Large & small deformation

20. Conclusions
Fission induced by peripheral heavy-ion collisions at relativistic energies, ideal conditions for the investigation of dissipation at small deformations
Determination of new observables
Total nuclear fission cross sections for different targets
Partial fission cross sections
Partial widths of the charge distributions of fission
fragments
Realistic description for f (t)
All observables described by a constant value of
 = 21021s f ≈ (1.7±0.4)10-21 s
(critical damping)
No indications for dependence on T or Z2/A
Evidence for strong increase of  with deformation

21. af/an

22. Fragmentation background

23. Transient time

24. Excitation energy vs. Z

25. Outlook