Aleksandra Kelić, Maria Valentina Ricciardi, Karl-Heinz SchmidtGSI – Darmstadt

Recent improvements in Recent improvements in the GSI fission modelthe GSI fission model

Task 11, subtask 3Task 11, subtask 3

http://www.gsi.de/charms/

Motivation 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?What do we need?

• Fission barriers

• Fragment distributions

• Level densities

• Nuclear viscosity

• Particle-emission widths

Fission competition in de-excitation of excited nuclei

E*

Mass and charge division in fissionMass and charge division in fission

Experimental information - High energyExperimental 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 energyExperimental 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

Available information:

- Z distributions at "one" energy

Experimental information - Low energy Experimental information - Low energy

Schmidt et al., NPA 665 (2000) 221

More than 70 secondary beams studied: from Z=85 to Z=92

Macroscopic-microscopic approachMacroscopic-microscopic approach

- Transition from single-humped to double-humped explained bymacroscopic and microscopic properties of the potential-energy landscape near outer saddle.

* Maruhn and Greiner, Z. Phys. 251 (1972) 431, PRL 32 (1974) 548; Pashkevich, NPA 477 (1988) 1;

Macroscopic part: property of CNMicroscopic part: properties of fragments*

N82

N90

Basic assumptions 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):

AA c

T2

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 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*

Calculations done by PashkevichA 132

A 140

Basic assumptions Basic assumptions 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 approachMacroscopic-microscopic approach

For each fission fragment we get:• Mass • Nuclear charge• Kinetic energy• Excitation energy• Number of emitted particles

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.

ABLA - evaporation/fission modelABLA - 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

- -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 dataComparison with data

ABLAABLA

Test of the evaporation part 56Fe (1 A GeV) + 1H

Data (C. Villagrasa et al, P. Napolitani et al)

INCL4+ABLA

Test of the fission part Fission probability 235Np

Data (A. Gavron et al., PRC13 (1976) 2374)

ABLA

Fission of secondary beams after the EM excitationFission of secondary beams after the EM excitation

89Ac

90Th

91Pa

92U

131

135

134

133

132

136

137

138

139

140

141

142

Black - experiment (Schmidt et al, NPA 665 (2000))

Red - calculations

With the same parameter set for all nuclei!

Neutron-induced fission of 238U for En = 1.2 to 5.8 MeVNeutron-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 scenarioMore complex scenario

238U+p at 1 A GeV

Model calculations (model developed at GSI):

Experimental data: