Micro-Macro Approach to Nuclear Fission: A Comprehensive Study

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) 014607; Bernas et al., NPA 765 (2006) 197; Armbruster et al., PRL 93 (2004) 212701; Taïeb et al., NPA 724 (2003) 413; Bernas et al., NPA 725 (2003) 213 www.gsi.de/charms/data.htm 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. E* What do we need? Fission competition in de-excitation of excited nuclei • • 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 www.gsi.de/charms/) 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. N  88 N  82 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* • 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. 92U 91Pa 142 140 141 90Th 138 139 89Ac 132 131 133 134 137 135 136 Fission of secondary beams after the EM excitation Black - experiment (Schmidt et al, NPA 665 (2000)) Red - calculations 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. Experimental data: Model calculations (BURST+ABLA07): More complex scenario 238U+p at 1 A GeV

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. Basic idea Experimental survey at GSI by use of secondary beams K.-H. Schmidt et al., NPA 665 (2000) 221 - 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.) • + Quantitative predictions for fission yields. • - 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.