1. Recent improvements in the GSI fission model
Task 11, subtask 3
Aleksandra Kelić, Maria Valentina Ricciardi, Karl-Heinz Schmidt
GSI – Darmstadt

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 fission and evaporation

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

4. Mass and charge division in fission

5. 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 2001
(see

6. Experimental information - Low energy
Particle-induced fission of long-lived targets and spontaneous fission
Available information:
- 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

7. Experimental information - Low energy
More than 70 secondary beams studied: from Z=85 to Z=92
Schmidt et al., NPA 665 (2000) 221

8. Macroscopic-microscopic approach
- Transition from single-humped to double-humped explained by
macroscopic and microscopic properties of the potential-energy landscape near outer saddle.
Macroscopic part: property of CN
Microscopic part: properties of fragments*
N82
N90
* Maruhn and Greiner, Z. Phys. 251 (1972) 431, PRL 32 (1974) 548; Pashkevich, NPA 477 (1988) 1;

9. Basic assumptions Macroscopic part:
Macroscopic potential is property of fissioning system ( ≈ f(ZCN2/ACN))
Potential near saddle from exp. mass distributions at high E* (Rusanov):
cA is the curvature of the potential at the
elongation where the decision on the A
distribution is made.
cA = f(Z2/A)  Rusanov*
* Rusanov et al, Phys. At. Nucl. 60 (1997) 683

10. Basic assumptions Microscopic part:
Microscopic corrections are properties of fragments (= f(Nf,Zf))
Assumptions based on shell-model calculations (Maruhn & Greiner, Pashkevich)
Shells near outer saddle "resemble" shells of final fragments (but weaker)
Properties of shells from exp. nuclide distributions at low E*
A  140
A  132
Calculations done by Pashkevich

11. Basic assumptions Mass of nascent fragments N/Z of nascent fragments
Dynamics:
Approximations based on Langevin calculations (P. Nadtochy):
τ (mass asymmetry) >> τ (saddle scission): decision near outer saddle
τ (N/Z) << τ (saddle scission) : decision near scission
Population of available states with statistical weight (near saddle or scission)
Mass of nascent fragments
N/Z of nascent fragments

12. Macroscopic-microscopic approach
Fit 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

13. ABLA - evaporation/fission model
Evaporation stage
- Extended Weisskopf approach with extension to IMFs
- Particle decay widths
- inverse cross sections based on nuclear potential
- thermal expansion of source
- angular momentum in particle emission
- g-emission at energies close to the particle threshold (A. Ignatyuk)
Fission
- Fission decay width
- analytical time-dependent approach (B. Jurado)
- double-humped structure in fission barriers
- symmetry classes in low-energy fission
- Particle emission on different stages of the fission process

14. Comparison with data

15. ABLA Test of the fission part  Fission probability 235Np
 Data (A. Gavron et al., PRC13 (1976) 2374)
 ABLA
Test of the evaporation part  56Fe (1 A GeV) + 1H
 Data (C. Villagrasa et al, P. Napolitani et al)
 INCL4+ABLA

16. 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!

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

18. More complex scenario 238U+p at 1 A GeV
Model calculations (model developed at GSI):
Experimental data: