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

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

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.

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

Mass and charge division in fission

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

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.

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* N  82 N  88 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

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

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

Comparison with data - With a fixed set of model parameters -

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!

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

ABLA07 – IMF emission Exp - R.Michel et al., NIM B129 (1997) 153 Calculations – BURST+ABLA, BURST+ABLA07

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

More complex scenario 238U+p at 1 A GeV Model calculations (BURST+ABLA07): Experimental data:

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

Additional slides

Experimental survey at GSI by use of secondary beams Basic idea Experimental survey at GSI by use of secondary beams K.-H. Schmidt et al., NPA 665 (2000) 221 How do we get information on micro macro...? - Transition from single-humped to double-humped explained by macroscopic and microscopic properties of the potential-energy landscape near outer saddle.

ABLA07 – Low-energy fission Test of the fission part  Fission probability 235Np  Data (A. Gavron et al., PRC13 (1976) 2374)  ABLA07

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

ABLA07 Test of the evaporation part  56Fe (1 A GeV) + 1H  Data (C. Villagrasa et al, P. Napolitani et al)  INCL4+ABLA07

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

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.

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.) - 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.