Recent improvements in the GSI fission model Task 11, subtask 3 Aleksandra Kelić, Maria Valentina Ricciardi, Karl-Heinz Schmidt GSI – Darmstadt http://www.gsi.de/charms/

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 fission and evaporation

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 2001 (see www.gsi.de/charms/)

Experimental information - Low energy 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 the stable targets EM fission of secondary beams at GSI - Z distributions at "one" energy

Experimental information - Low energy More than 70 secondary beams studied: from Z=85 to Z=92 Schmidt et al., NPA 665 (2000) 221

Macroscopic-microscopic approach - Transition from single-humped to double-humped explained by macroscopic and microscopic properties of the potential-energy landscape near outer saddle. Macroscopic part: property of CN Microscopic part: properties of fragments* N82 N90 * Maruhn and Greiner, Z. Phys. 251 (1972) 431, PRL 32 (1974) 548; Pashkevich, NPA 477 (1988) 1;

Basic assumptions Macroscopic part: Macroscopic potential is property of fissioning system ( ≈ f(ZCN2/ACN)) Potential near saddle from exp. mass distributions at high E* (Rusanov): cA is the curvature of the potential at the elongation where the decision on the A distribution is made. cA = f(Z2/A)  Rusanov* * Rusanov et al, Phys. At. Nucl. 60 (1997) 683

Basic assumptions Microscopic part: Microscopic corrections are properties of fragments (= f(Nf,Zf)) Assumptions based on shell-model calculations (Maruhn & Greiner, Pashkevich) Shells near outer saddle "resemble" shells of final fragments (but weaker) Properties of shells from exp. nuclide distributions at low E* A  140 A  132 Calculations done by Pashkevich

Basic assumptions Mass of nascent fragments N/Z of nascent fragments Dynamics: Approximations based on Langevin calculations (P. Nadtochy): τ (mass asymmetry) >> τ (saddle scission): decision near outer saddle τ (N/Z) << τ (saddle scission) : decision near scission Population of available states with statistical weight (near saddle or scission) Mass of nascent fragments N/Z of nascent fragments

Macroscopic-microscopic approach Fit 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

ABLA - evaporation/fission model Evaporation stage - Extended Weisskopf approach with extension to IMFs - Particle decay widths - inverse cross sections based on nuclear potential - thermal expansion of source - angular momentum in particle emission - g-emission at energies close to the particle threshold (A. Ignatyuk) Fission - Fission decay width - analytical time-dependent approach (B. Jurado) - double-humped structure in fission barriers - symmetry classes in low-energy fission - Particle emission on different stages of the fission process

Comparison with data

ABLA Test of the fission part  Fission probability 235Np  Data (A. Gavron et al., PRC13 (1976) 2374)  ABLA Test of the evaporation part  56Fe (1 A GeV) + 1H  Data (C. Villagrasa et al, P. Napolitani et al)  INCL4+ABLA

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 - ABLA calculations

More complex scenario 238U+p at 1 A GeV Model calculations (model developed at GSI): Experimental data: