Aleksandra Kelic, Maria Valentina Ricciardi, KarlHeinz Schmidt

1
Microscopic-macroscopic approach to the nuclear
fission process

• Aleksandra Kelic, Maria Valentina Ricciardi,
  Karl-Heinz Schmidt
• GSI Darmstadt

http//www.gsi.de/charms/
2
Outline
- Why studying fission Basic research Applicati
ons (astrophysics, RIB production, spallation
sources...)
- Mass and charge distributions Experimental
information GSI model ABLA
- Fission barriers of exotic nuclei Test of
isotopic trends of different models
- Summary and outlook
3
Motivation
Basic research Fission corresponds to a
large-scale collective motion where both static
and dynamic properties play important role

• Excellent tool to study, e.g.
• Nuclear structure effects at large deformations
• Fluctuations in charge polarisation
• Viscosity of nuclear matter

4
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
5
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
S. Wanajo et al., NPA 777 (2006) 676
Challenge - fission properties (e.g. fission
barriers, fission-fragment distributions) for
nuclei not accessible in laboratory.
6
What do we need?
Fission competition in de-excitation of excited
nuclei

• Fission barriers
• Fragment distributions
• Level densities
• Nuclear viscosity
• Particle-emission widths

7
Mass and charge division in fission
8
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/)
9
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
• Available information
• - Z distributions at "one" energy

10
Experimental information - Low energy
More than 70 secondary beams studied from Z85
to Z92
Schmidt et al., NPA 665 (2000) 221
11
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
Maruhn and Greiner, Z. Phys. 251 (1972) 431,
PRL 32 (1974) 548 Pashkevich, NPA 477 (1988) 1
12
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
13
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
14
Basic assumptions

• Dynamics
• Approximations based on Langevin calculations (P.
  Nadtochy)
• t (mass asymmetry) gtgt t (saddle scission)
  decision near outer saddle
• t (N/Z) ltlt t (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
15
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

16
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

17
Comparison with data
18
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) ? INCL4ABLA
19
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!
20
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
21
More complex scenario
238Up at 1 A GeV
22
Fission barriers
Difficulties when extrapolating in unknown
regions (e.g. r-process, super-heavies)
23
Fission barriers - Experimental information
Relative uncertainty gt10-2
Available data on fission barriers, Z 80
(RIPL-2 library)
24
Fission barriers - Experimental information
Fission barriers Relative uncertainty gt10-2
GS masses Relative uncertainty 10-4 - 10-9
Courtesy of C. Scheidenberger (GSI)
25
Experiment - Difficulties

• Experimental sources
• Energy-dependent fission probabilities
• Extraction of barrier parameters
• Requires assumptions on level densities

Gavron et al., PRC13 (1976) 2374
26
Experiment - Difficulties
Extraction of barrier parameters Requires
assumptions on level densities!
Gavron et al., PRC13 (1976) 2374
27
Theory

• Recently, important progress on calculating the
  potential surface using microscopic approach
  (e.g. groups from Brussels, Goriely et al
  Bruyères-le-Châtel, Goutte et al Madrid, Pèrez
  and Robledo ...)
• - Way to go!
• - But, not always precise enough and still very
  time consuming

• Another approach ? microscopic-macroscopic
  models (e.g. Möller et al Myers and Swiatecki
  Mamdouh et al ...)

28
Theory - Difficulties
Dimensionality (Möller et al, PRL 92) and
symmetries (Bjørnholm and Lynn, Rev. Mod. Phys.
52) of the considered deformation space are very
important!
Reflection symmetric
Reflection asymmetric
Limited experimental information on the height
of the fission barrier ? in any theoretical model
the constraint on the parameters defining the
dependence of the fission barrier on neutron
excess is rather weak.
29
Open problem

• Limited experimental information on the
  height of the fission barrier

Kelic and Schmidt, PLB 643 (2006)
30
Idea
Predictions of theoretical models are examined by
means of a detailed analysis of the isotopic
trends of saddle-point masses.
?Usad ? Empirical saddle-point shell-correction
energy
31
Idea

What do we know about saddle-point
shell-correction energy?
1. Shell corrections have local character
2. Shell-correction energy at SP should be very
small (e.g Myers and Swiatecki PRC 60 (1999)
Siwek-Wilczynska and Skwira, PRC 72 (2005))
1-2 MeV
If an model is realistic ? Slope of ?Usad as
function of N should be 0 Any general trend
would indicate shortcomings of the model.
32
Studied models

• 1) Droplet model (DM) Myers 1977, which is a
  basis of often used results of the Howard-Möller
  fission-barrier calculations HowardMöller 1980
• 2) Finite-range liquid drop model (FRLDM) Sierk
  1986, Möller et al 1995
• 3) Thomas-Fermi model (TF) Myers and Swiatecki
  1996, 1999
• 4) Extended Thomas-Fermi model (ETF) Mamdouh et
  al. 2001

Myers, Droplet Model of Atomic Nuclei, 1977
IFI/Plenum Howard and Möller, ADNDT 25 (1980)
219. Sierk, PRC33 (1986) 2039. Möller et al,
ADNDT 59 (1995) 185. Myers and Swiatecki, NPA
601( 1996) 141 Myers and Swiatecki, PRC 60
(1999) 0 14606-1 Mamdouh et al, NPA 679 (2001) 337
33
Example for uranium
?Usad as a function of a neutron number
A realistic macroscopic model should give almost
a zero slope!
34
Results
Slopes of dUsad as a function of the neutron
excess
? The most realistic predictions are expected
from the TF model and the FRLD model ? Further
efforts needed for the saddle-point mass
predictions of the droplet model and the extended
Thomas-Fermi model
Kelic and Schmidt, PLB 643 (2006)
35
Conclusions
- Good description of mass and charge division in
fission based on a macroscopic-microscopic
approach, which allows for robust
extrapolations - According to a detailed
analysis of the isotopic trends of saddle-point
masses indications have been found that the
Thomas-Fermi model and the FRLDM model give the
most realistic predictions in regions where no
experimental data are available - Need for more
precise and new experimental data using new
techniques and methods (e.g. R3B and ELISE at
FAIR) ? basis for further developments in theory