1. Microscopic-macroscopic approach to the nuclear fission process
Aleksandra Kelić, Maria Valentina Ricciardi, Karl-Heinz Schmidt
GSI – Darmstadt
- Motivation
- Mass and charge division in fission
- ABLA07
- Comparison with experimental data

2. Motivation RIB production (fragmentation method, ISOL method),
Spallation sources and ADS
Data measured at FRS*
* Ricciardi et al, PRC 73 (2006) ; Bernas et al., NPA 765 (2006) 197; Armbruster et al., PRL 93 (2004) ; Taïeb et al., NPA 724 (2003) 413; Bernas et al., NPA 725 (2003) 213
Challenge - need for consistent global description of low- and high-energy fission and evaporation

3. Motivation Astrophysics - r-process and nucleosynthesis
-Trans-uranium elements 1)
- r-process endpoint 2)
- Fission cycling 3)
1) Cowan et al, Phys. Rep. 208 (1991) 267;
2) Panov et al., NPA 747 (2005) 633
3) Seeger et al, APJ 11 Suppl. (1965) S121
4) Rauscher et al, APJ 429 (1994) 49
Challenge - fission properties (e.g. fission barriers, fission-fragment distributions) for nuclei not accessible in laboratory.

4. What do we need?
Fission competition in de-excitation of excited nuclei E*
• Fission barriers
Fragment distributions
• Level densities
• Nuclear viscosity
Particle-emission widths

5. Mass and charge division in fission

6. Experimental information - High energy
In cases when shell effects can be disregarded, the fission-fragment mass distribution is Gaussian 
Data measured at GSI:
T. Enqvist et al, NPA 686 (2001) 481
(see
Large systematic on sA by Rusanov et al, Phys. At. Nucl. 60 (1997) 683

7. Experimental information - Low energy
Particle-induced fission of long-lived targets and spontaneous fission:
- A(E*) in most cases
- A and Z distributions of light fission group only in the thermal-neutron induced fission on the stable targets
EM fission of secondary beams at GSI:
- Z distributions at "one" energy
Transition from single-humped to double-humped explained by
macroscopic and microscopic properties of the potential-energy landscape near outer saddle.

8. Basic assumptions Macroscopic part:
Given by properties of fissioning nucleus
Potential near saddle from exp. mass distributions at high E* (1):
Microscopic part:
Shells near outer saddle "resemble" shells of final fragments (but weaker) (2)
Properties of shells from exp. nuclide distributions at low E*
N  82
N  88
Dynamics:
Approximations based on Langevin calculations (3):
Mass asymmetry: decision near outer saddle
N/Z: decision near scission
(1) Rusanov et al, Phys. At. Nucl. 60 (1997) 683
(2) Maruhn and Greiner, PRL 32 (1974) 548; Pashkevich, NPA 477 (1988) 1;
Pashkevich et al.
(3) P. Nadtochy, private communiation

9. Macroscopic-microscopic approach
Model parameters:
Curvatures, strengths and positions of two microscopic contributions as free parameters
These 6 parameters are deduced from the experimental fragment distributions and kept fixed for all systems and energies.
For each fission fragment we get:
Mass
Nuclear charge
Kinetic energy
Excitation energy
Number of emitted particles
N  82
N  88

10. ABLA07 - evaporation/fission model
Evaporation stage
- Emission of IMFs (sequential and simultaneous) (Poster: M.V. Ricciardi)
- Particle decay widths:
- energy-dependent inverse cross sections based on nuclear potential
- thermal expansion of emitting source
- angular momentum in particle emission
- g-emission at energies close to the particle threshold (A.V. Ignatyuk, 2002)
Fission
- Influence of nuclear viscosity on the fission decay width:
- analytical time-dependent approach (B. Jurado et al, 2003)
- influence of initial conditions
- Particle emission on different stages of the fission process

11. Comparison with data
- With a fixed set of model parameters -

12. Fission of secondary beams after the EM excitation
Black - experiment (Schmidt et al, NPA 665 (2000))
Red - calculations
89Ac
90Th
91Pa
92U
131
135
134
133
132
136
137
138
139
140
141
142
With the same parameter set for all nuclei!

13. Neutron-induced fission of 238U for En = 1.2 to 5.8 MeV
Data - F. Vives et al, Nucl. Phys. A662 (2000) 63; Lines – ABLA07 calculations

14. ABLA07 – IMF emission Exp - R.Michel et al., NIM B129 (1997) 153
Calculations – BURST+ABLA, BURST+ABLA07

15. ABLA07 - Particle decay width
 exp - R.Michel et al., NIM B103; C.M.Herbach et al., Proc. of the SARE-5 meeting, 2000
BURST+ABLA07 – Only contribution from evaporation

16. More complex scenario 238U+p at 1 A GeV
Model calculations (BURST+ABLA07):
Experimental data:

17. Conclusions
- Good description of mass and charge division in low-energy fission based on a macroscopic-microscopic approach
- Good descriptions of more complex scenarios (i.e. spallation reactions)
 Allows for robust extrapolation in experimentally unexplored
regions.
- Next step – coupling with INCL4.4

18. Additional slides

19. Experimental survey at GSI by use of secondary beams
Basic idea
Experimental survey at GSI by use of secondary beams
K.-H. Schmidt et al., NPA 665 (2000) 221
How do we get information on micro macro...?
- Transition from single-humped to double-humped explained by
macroscopic and microscopic properties of the potential-energy landscape near outer saddle.

20. ABLA07 – Low-energy fission
Test of the fission part  Fission probability 235Np
 Data (A. Gavron et al., PRC13 (1976) 2374)
 ABLA07

21. Comparison with data - spontaneous fission
Experiment
Calculations
(experimental resolution not included)

22. ABLA07 Test of the evaporation part  56Fe (1 A GeV) + 1H
 Data (C. Villagrasa et al, P. Napolitani et al)
 INCL4+ABLA07

23. Particle emission widths
Extended Weißkopf-Ewing formalism
Barriers 
based on Bass potential (empirically deduced from fusion)
Inverse cross section 
energy-dependent inverse cross sections
→ ingoing-wave boundary condition model
tunnelling through the barrier
Angular momentum 
change in angular momentum due to particle emission

24. IMF Emission
All nuclei below the Businaro-Gallone maximum of the mass-asymmetry dependent barrier are taken into account in the evaporation process  natural transition between fission and evaporation picture.
The barriers are given by the Bass nuclear potential.

25. Theory
Strutinsky-type calculations of the potential-energy landscape (e.g. P. Möller)
+ Good qualitative overview on multimodal character of fission.
- No quantitative predictions for fission yields.
- No dynamics
Statistical scission-point models (e.g. Fong, Wilkins et al.)
+ Quantitative predictions for fission yields.
- No memory on dynamics from saddle to scission.
Statistical saddle-point models (e.g. Duijvestijn et al.)
- Neglecting dynamics from saddle to scission.
- Uncertainty on potential energy leads to large uncertainties in the yields.
Time-dependent Hartree-Fock calculations with GCM (Goutte)
+ Dynamical and microscopic approach.
- No dissipation included.
- High computational effort.