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 s A 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 saddle.

of the potential energy landscape near outer

Basic assumptions

Macroscopic part:

Given by properties of fissioning nucleus • Potential near saddle from exp. mass distributions at high E* (1) :

c A

 s

T

2

A



F

(

A CN

,

Z CN

)

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) (2) (3) Rusanov et al, Phys. At. Nucl. 60 (1997) 683 Maruhn and Greiner, PRL 32 (1974) 548; Pashkevich, NPA 477 (1988) 1; P. Nadtochy, private communiation N  Pashkevich et al.

N  82 88

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.

N  82 N  88 For each fission fragment we get: • Mass • Nuclear charge • Kinetic energy • Excitation energy • Number of emitted particles

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 92 U 91 Pa 142 140 141 90 Th 89 Ac 131 132 133 134 135 136 137 138 139 With the same parameter set for all nuclei!

Neutron-induced fission of 238 U 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

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

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

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.

ABLA07 – Low-energy fission

Test of the fission part  Fission probability 235 Np  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  56 Fe (1 A GeV) + 1 H  Data (C. Villagrasa et al, P. Napolitani et al)  INCL4+ABLA07

Particle emission widths

Extended Weißkopf-Ewing formalism    

i

 2  2  π 

s

   1  

i

 2 π  

m

  2 

E i

  0

S

 s

c

   

f

    

B

  d

E f

• Barriers   based on Bass potential (empirically deduced from fusion) • Inverse cross section   energy-dependent inverse cross sections → i ngoing-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.) + 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.