Experimental knowledge on nuclear fission analyzed with a semi-empirical ordering scheme

1. Experimental knowledge on nuclear fissionanalyzed with a semi-empirical ordering scheme Karl-Heinz Schmidt, Aleksandra Kelić, Maria Valentina Ricciardi GSI-Darmstadt, Germany http://www.gsi.de/charms/ Supported by the European Union withinHINDAS, 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 0 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. Mpre F Observables Large variety of observables: - 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 - ... - 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 AandZ 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 www.gsi.de/charms/) 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 andspontaneous fission • Available information: • - A(E*) in most cases • - A and Z distributions of lightfission group only in thethermal-neutron induced fissionon stable targets • EM fission of secondary beams at GSI • Available information: • - 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. Exp data measured at GSI Assumption 1 – Statistical model - Mass / element yield is proportional to the available phase space : - 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. 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  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. 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 - Particleemission on different stages

23. 92U 91Pa 142 140 141 90Th 138 139 89Ac 132 131 133 134 137 135 136 Multimodal fission around 226Th 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, NPA617 Walsh et al, NPA 276 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 ofnuclide yields andmoments. (M. V. Ricciardi et al., PRC 73 (2006) 014607) 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)