1. Experimental knowledge on nuclear fission analyzed with a semi-empirical ordering scheme
Karl-Heinz Schmidt, Aleksandra Kelić,
Maria Valentina Ricciardi
GSI-Darmstadt, Germany
Supported by the European Union within HINDAS, EUROTRANS, EURISOL_DS

2. Overview Brief overview on fission experiments
Available information on mass and element distributions of fission fragments
How can we classify measured data?

3. Different 'faces' of the fission process
~3Af MeV
Multifragmentation  'end' of fission
Transient effects
~ 150 MeV
High-energy fission
À la liquid drop
Dissipative phenomena
Excitation energy
Symmetric fission
~ 40 MeV
Dissipation in a superfluid Fermionic system
Low-energy fission
Nuclear-structure effects
~ Bf
Resonance phenomena
Spontaneous fission

4. Mechanisms to induce fission
- Neutron-induced fission
(e.g. ILL Grenoble, IRMM, Jyväskylä, Los Alamos, nTOF...)
- Particle (p, anti-p, p, m) induced fission
(e.g. Jyväskylä, PNPI, GSI, CERN ...)
- Photofission
(e.g. CEA, Kurchatov institute, IPNO, GSI, CERN...)
- Transfer and deep-inelastic reactions
(e.g. Los Alamos, Grenoble, IPNO, GANIL ...)
- Heavy-ion induced fission
(e.g. Canberra, KVI, IPHC, GSI...)

5. Observables Large variety of observables: Mpre F
- Fission cross sections
- Pre-scission particle and g multiplicities
- Angular anisotropies
- Mass distribution of fragments
- Charge distribution of fragments
- Spin distribution of fragments
- Post-scission particle and g multiplicities
- TKE
- ... F
Mpre
- Different observables "determined" at different moments along the fission process  enables probing of different stages of fission process

6. Experimental difficulties
- Restricted choice of systems
Available targets  stable or long-lived nuclei
Secondary beams  no beams above 238U by fragmentation
Reaction products  limited N/Z range in heavy-ion fusion
- Physical limits on resolution
Z and A resolution difficult at low energies
Scattering in target/detector at low energies (tails in A/TKE distribution)
- Restriction to specific mechanisms to induce fission in available
installations
Lohengrin: only thermal neutrons
FRS: only Coulomb fission or fragmentation-fission reactions
Fusion: high E* and spin or spontaneous fission
- Technical limits on correlations (limitations of available installations)
FRS detects only fission fragments at zero degree, no neutrons, no g
No experimental information available on A and Z of both fission fragments
simultaneously

7. Overview on available mass and element
distributions of fission fragments

8. 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

9. Experimental information – Low-energy fission
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 stable targets
EM fission of secondary beams at GSI
- Z distributions at energy of GDR (E* ≈ 11 MeV)

10. Experimental information – Low-energy fission
Mass – TKE distributions usually fitted in the frame of three fission modes (superlong, standard 1, standard 2)
n(1.7 MeV) + 238U:

11. Classification Macro-microscopic approach exploiting the separation of
compound nucleus and fragment properties
on the fission path.
Basic concept: Yields proportional to available states on the fission path.

12. Assumption 1 – Statistical model
- Mass / element yield is proportional to the available phase space :
Exp data measured at GSI
- At which point one should apply statistical model to calculate mass distributions?
Langevin calculations*  Somewhere between saddle and scission.
* Addev et al, NPA 502, p.405c, T. Asano et al, JNRS 7, p.7

13. Assumption 2 - Preformation hypothesis
U. Mosel and H. W. Schmitt, NPA 165 (1971) 73:
“By analyzing the single-particle states along the fission path .. we have established the fact that the influence of fragment shells reaches far into the PES. The preformation of the fragments is almost completed already at a point where the nuclear shape is necked in only to 40 %.“
Potential-energy surface of 224Th calculated by Pashkevich.
Conclusion: Shells on the fission path are a function of N and Z of the fragments!

14. What to do?
 Use statistical model to correlate measured mass / element
distributions with nuclear potential
 Apply statistical model close beyond the outer saddle
 Mass-asymmetric nuclear potential is given by two contributions:
Macroscopic given by the properties of the fissioning system
Microscopic given by the properties of fission fragments

15. Macroscopic potential - experimental systematics
Experiment: In cases when shell effects can be disregarded (high E*), the fission-fragment mass distribution of heavy systems is Gaussian.
Second derivative of potential in mass asymmetry deduced from width of fission-fragment mass distributions.
σA2 ~ T/(d2V/dη2)
← Mulgin et al. NPA 640 (1998) 375
Width of mass distribution is empirically well established. (M. G. Itkis, A.Ya. Rusanov et al., Sov. J. Part. Nucl. 19 (1988) 301 and Phys. At. Nucl. 60 (1997) 773)

16. Measured element yields
Microscopic features
Measured element yields
K.-H. Schmidt et al., NPA 665 (2000) 221
Potential-energy landscape (Pashkevich)
Extension of the statistical model to multimodal fission:
Yields of fission channels ~ number of states in the fission valleys

17. Microscopic potential deduced from A distribution
M. G. Itkis et al., Sov. J. Nucl. Phys. 43 (1986) 719
Input: - Experimental yields and - „Macroscopic“ yields
Result: - Shell-correction energy

18. Microscopic potential deduced from A distribution
M. G. Itkis et al., Sov. J. Nucl. Phys. 43 (1986) 719
Symbols - "experimental" shell corrections
Line – theoretical shell correction (A.V. Pashkevich)
Conclusion: Shell corrections have “universal” character.
Limited to only few systems, and shell corrections considered in mass only

19. Microscopic potential of other systems
A(macroscopic)
Teff
226Th (E* ≈ 11 MeV)
8.8
0.6 MeV
238U(n,f), En = 1.7 MeV
9.5
0.4 MeV
252Cf (spont. fission)
11.3
260Md (spont. fission)
12.2
 Parameters used to deduce microscopic contribution
Shape of microscopic potential varies drastically.

20. Shells of fragments
Importance of spherical and deformed neutron shells
Wilkins et al.
PRC 14 (1976) 1832

21. Test case: fission modes from 226Th to 260Md
Simplified illustration: Schematic decomposition of microscopic structure by N = 82 (Standard 1) and N ≈ 92 (Standard 2) shells, only. Same shell parameters for all cases.
Shell
Depth
Width (σA)
N = 82
-3.3 MeV
3.5
N = 92
-4.0 MeV
7.0
Global features of microscopic structure are reproduced.

22. Test case: multi-modal fission around 226Th
These ideas represent the basis of the GSI semi-empirical fission model.
Additional content:
- Influence of the proton Z=50 shell on the Standard 1 mode
- Decreasing strength of combined Z=50 and N=82 shells when
going away from A=132 (obtained from GS shell-correction
energy)
- Charge polarisation effects
- Particle emission on different stages

23. Multimodal fission around 226Th
89Ac
90Th
91Pa
92U
131
135
134
133
132
136
137
138
139
140
141
142
Black: experimental data (GSI experiment) Red: model calculations (N=82, Z=50, N=92 shells)

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

25. Other observables Spontaneous fission of 252Cf Mass: Neutrons: TKE:
Line: Model calculations
Data:
Hambsch et al, NPA Walsh et al, NPA Zakharova et al,
Wahl, ADNDT 39

26. Future Electron-ion collider ELISE of FAIR project of GSI, Darmstadt.
(Rare-isotope beams + tagged photons)
Aim: Precise fission data over large N/Z range.

27. Conclusions
- Using a semi-empirical ordering scheme based on the macro-microscopic approach and the separability of compound-nucleus and fragment properties along the fission path a large portion of common features behind the variety of the complex observation has been revealed.
- While separate calculations of shell effects or separate microscopic calculations for the different fissioning systems suffer from individual numerical uncertainties attributed to every single system, the separability principle suggests that the shell effects are essentially the same for all fissioning systems.
- Good bases for modelling the fission process.

28. Influence of experimental geometry

29. Comparison with 238U (1 A GeV) + 1H
Full calculation with ABRABLA07 code (description of fission included)
Comparison of nuclide yields and moments.
(M. V. Ricciardi et al., PRC 73 (2006) )
ABRABLA07: Monte-Carlo code, abrasion, multifragm. continuous emission of n, LCP, IMF, fission (transients, Nf,Zf,TKE, evaporation pre, post)

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