1. Fission cross sections and the dynamics of the fission process F. -J
Fission cross sections and the dynamics of the fission process F.-J. Hambsch

2. Overview Introduction Multi-Modal Random Neck Rupture (MM-RNR) model
Statistical modeling of reaction cross sections
Prediction of fission mode fluctuations
Preliminary experimental results on 238U(n,f)
Conclusions

3. Joint Research Center (JRC)
Founded in 1957 under the Treaty of Rome.
Opened on May 16, 1960.
Five scientific research units and two support groups with a total staff of approximately 350 persons.

4. Introduction Mono-energetic neutron source
7 MV Van-de-Graaff accelerator
7LiF(p,n)7Be, TiT(p,n)3He, D2(d,n)3He, TiT(d,n)4He
DC (Ip,d < 50 A), pulsed beam available
non-T beam line
n < 109 /s/sr
ionisation chambers, NE213 neutron/gamma-ray detectors, BF3 counters, HPGe detectors
Bonner spheres
fast rabbit systems (T1/2 > 1s) for activation studies

5. Introduction (cont.) GELINA neutron TOF spectrometer
MeV electron accelerator
repetition frequency: Hz
neutron pulse: 2 s - 1 FWHM
n = Hz
12 different flight paths with a length between 8 and 400 m
ionisation chambers, C6D6 detectors
high-resolution -ray detectors
fission chambers for flux monitoring

6. Introduction (cont.)
For a successful design of nuclear applications the precise knowledge of the involved reaction cross- sections is a pre-requisite
cross-section data measurements  point wise data
cross-section data evaluation  nuclear reaction models
Successful modelling of reaction cross-section data requires precise knowledge about the nuclear physics involved. In case of nuclear fission (n- or x-particle induced)
shape of the nuclear energy landscape
probability of competing reaction mechanisms

7. The OECD nuclear data network
IAEA - INDC
WPEC
JEFF
ENDF
JENDL
CENDL
BROND
NEA Databank
Nuclear Energy Agency
Nucl. Sci. Committee
WPEC:
Working Party for
Evaluation Co-operation
JEFF:
Joint European
Fission + Fusion datafile

8. Modelling Scission point configuration(s): AFF, TKE Fission modes ???
Nuclear energy landscape
fission valleys (fission modes)
fission barrier height and penetrability: EA, EB, hA, hB
ground state properties: EI, EII
(hyper-deformation: EC, hC, EIII)
Quantitative predictions of FF characteristics Y(A,TKE, p, d, ...)

9. Fission within the MM-RNR model (Multi-Modal Random Neck-Rupture)
Lawrence shapes
Dumbbell representation
geometric parameters (l,r,s,z,c)
several fission modes
common inner barrier
individual outer barriers
mode-specific scission configurations
fission-fragment deformation
fission-fragment intrinsic excitation
Potential energy surface
U. Brosa, S. Grossmann and A. Müller, Physics Report 197 (1990) 167
S. Oberstedt, F.-J. Hambsch and F. Vives, Nucl. Phys. A644 (1998) 289

10. Calculated fission modes (239U)

11. Fission modes in nuclear fission ?
parameterisation in terms of two asymmetric and one symmetric fission modes quite successful for the fission of the CN 236,239U and 240Pu
including fission modes into fission cross-section models  quantitative description of FF emission yields
for 252Cf (SF) more modes necessary !???

12. Mass distribution and modal fit

13. TKE distribution and modal fit

14. Statistical Model
Below second chance fission the neutron interaction takes place through direct and compound nuclear mechanisms. Beside fission the following processes are possible : elastic and inelastic scattering and radiative capture.
For the direct mechanism the coupled channel method (ECIS code) is used and for compound nuclear mechanism a statistical model (STATIS code which takes into account sub- barrier effects and the multi-modal fission concept) is used.

15. ECIS code provides: Raynal J.
Statistical Model II
ECIS code provides: Raynal J.
STATIS code provides:
Vladuca G., Tudora A.,
Hambsch F.-J., Oberstedt S.,
Nucl.Phys. A707, 32 (2002)

16. Schematic View of Barrier Structure

17. Total cross section calculation

18. Elastic cross section

19. Differential elastic cross section

20. Differential elastic cross section

21. Differential elastic cross section

22. Inelastic cross section

23. Differential inelastic cross section

24. Radiative capture cross section

25. 235U(n,f) cross section of the S2 mode and total

26. Resonance region of 231Pa

27. Fission Cross-section for 238U(n,f)

28. Branching Ratio for 238U(n,f)

29. 235U Mass Distribution at En=1.0 MeV

30. 238U Mass Distribution at En=1.2 MeV

31. 238U Mass Distribution at En=0.9 MeV

32. “Fission-mode fluctuations in a resonance”
further experiments in summer 2006
more data being analysed (PhD thesis)
En (MeV)
fission cross-section (b)

33. Quality of measurements

34. Comparison to Vives et al.

35. Data analysis

36. Parasitic reactions cross sections
13.6 mb
276 mb
25% Photo fission events at En=0.9 MeV, estimation on Total cross section
39 mb * 3
7.9 mb
11.6 mb

37. Conclusions
Statistical model calculations reproduce very well the different reaction cross sections
Inclusion of fission modes adds additional predicting power to the model
Experimental verification of fission mode changes under way for 238U(n,f)
Preliminary data show variations of fission fragment properties at vibrational resonances in 238U(n,f)

39. Consistency of results ?
From barrier parameters calculation of fission isomers fails
Barrier parameters from fission cross-section analysis are in contradiction with those following from resonance parameters obtained for intermediate structure resonances
3rd minimum (HD) experimentally confirmed for 234U (Krasnahorkay et al.)

40. Motivation
IRMM has longstanding tradition in measuring fission fragment properties and cross-sections.
Experimental data are well described within the multi-modal fission model.
Evaluation activity (and experimental activity) is diminishing.
New evaluation approach based on model calculations with experimental input parameters.
Prediction of fission fragment mass yield distributions.

41. Statistical Model III
From the former relations it is obvious that correct calculations for the compound nucleus (fission, radiative capture, elastic and inelastic CN cross-sections) need good direct interaction calculations.
The coupled channel parameters are determined in such a way to obtain the best possible agreement of the “direct” calculations with the total experimental cross- section and with experimental (differential) elastic and inelastic cross-sections at incident neutron energies E3 MeV, where the compound nucleus contributions is very small and can be neglected.