Microscopic-macroscopic approach to the nuclear fission process

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Microscopic-macroscopic approach to the nuclear
fission process

• Aleksandra Kelic and Karl-Heinz Schmidt
• GSI-Darmstadt, Germany
• http//www.gsi.de/charms/

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Overview

• Why studying fission?
• What is the needed input?
• Mass and charge distributions in fission
• ? GSI semi-empirical model
• Saddle-point masses
• ? Macroscopic-microscopic approaches
• Conclusions

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Why is fission interesting?
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Energy production
- Fission reactors - Accelerator-driven systems
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RIB production
Fragmentation method, ISOL method
Data measured at GSI
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
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Astrophysics
TransU elements ? 1)
r-process endpoint ? 2)
Fission cycling ? 3, 4)
S. Wanajo et al., NPA 777 (2006) 676
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
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Basic science
Fission corresponds to a large-scale collective
motion
N. Carjan et al, NPA452
Both static (e.g. potential) and dynamic (e.g.
viscosity) properties play important role

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

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What do we need?
Fission competition in de-excitation of excited
nuclei

• Height of fission barriers
• Fragment distributions
• Level densities
• Nuclear viscosity

• Height of fission barriers
• Fragment distributions
• Level densities
• Nuclear viscosity

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Mass and charge division in fission
- Available experimental information -
Modelisation - GSI model
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Experimental information - High energy
In cases when shell effects can be disregarded,
the fission-fragment mass distribution is
Gaussian ?
Data measured at GSI M. Bernas et al, J. Pereira
et al, T. Enqvist et al (see www.gsi.de/charms/)
Width of mass distribution is empirically well
established (M. G. Itkis, A.Ya. Rusanov et al.,
Sov. J. Part. Nucl. 19 (1988) 301 and Phys. At.
Nucl. 60 (1997) 773)
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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

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Experimental information - Low energy
Experimental survey at GSI by use of secondary
beams
K.-H. Schmidt et al., NPA 665 (2000) 221
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How can we describe experimental data?
? Empirical systematics on A or Z distributions -
Problem is often too complex
?Theoretical models - Way to go, but not always
precise enough and still very time consuming

• Encouraging progress in a full microscopic
  description of fission
• H. Goutte et al., PRC 71 (2005) ? Time-dependent
  HF calculations with GCM

? Semi-empirical models - Theory-guided
systematics
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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
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Basic assumptions
Basic ideas of our macroscopic-microscopic
fission approach (Inspired by Smirenkin, Maruhn,
Pashkevich, Rusanov, Itkis, ...)
Macroscopic Potential near saddle from exp.
mass distributions at high E (Rusanov) Macroscopi
c potential is property of fissioning system (
f(ZCN2/ACN))
Microscopic 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 Microscopic corrections are properties of
fragments ( f(Nf,Zf))
Dynamics Approximations based on Langevin
calculations (P. Nadtochy) t (mass asymmetry) gtgt
t (saddle scission) decision near saddlet (N/Z)
ltlt t (saddle scission) decision near
scission Population of available states with
statistical weight (near saddle or scission)
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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

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Comparison with EM data
Fission of secondary beams after the EM
excitation black - experiment red - calculations
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Comparison with high-energy data

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Comparison with data
How does the model work in more complex
scenario? 238Up at 1 A GeV
Model calculations (model developed at GSI)
Experimental data
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Applications in astrophysics
Usually one assumes a) symmetric split AF1
AF2 b) 132Sn shell plays a role AF1 132, AF2
ACN - 132
But! Deformed shell around A140 can play in some
cases a dominant role!
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Saddle-point masses
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How well do we understand fission?

• Influence of nuclear structure (shell
  corrections, pairing, ...)

LDM
LDMShell
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Fission barriers - Experimental information
Relative uncertainty gt10-2
Available data on fission barriers, Z 80
(RIPL-2 library)
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Fission barriers - Experimental information
Fission barriers Relative uncertainty gt10-2
GS masses Relative uncertainty 10-4 - 10-9
Courtesy of C. Scheidenberger (GSI)
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Experiment - Difficulties

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

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

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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.
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Open problem

• Limited experimental information on the
  height of the fission barrier

Kelic and Schmidt, PLB 643 (2006)
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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
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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.
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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) MyersSwiatecki
  1996, 1999
• 4.) Extended Thomas-Fermi model (ETF) Mamdouh et
  al. 2001

W.D. Myers, Droplet Model of Atomic Nuclei,
1977 IFI/Plenum W.M. Howard and P. Möller, ADNDT
25 (1980) 219. A. Sierk, PRC33 (1986) 2039. P.
Möller et al, ADNDT 59 (1995) 185. W.D. Myers
and W.J. Swiatecki, NPA 601( 1996) 141 W.D.
Myers and W.J. Swiatecki, PRC 60 (1999) 0
14606-1 A. Mamdouh et al, NPA 679 (2001) 337
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Example for uranium
?Usad as a function of a neutron number
A realistic macroscopic model should give almost
a zero slope!
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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)
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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 ? basis for further
developments in theory - Need for close
collaboration between experiment and theory
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Additional slides
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Comparison with data - spontaneous fission

Experiment
Calculations (experimental resolution not
included)
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Macroscopic-microscopic approach

K.-H. Schmidt et al., NPA 665 (2000) 221
Calculations done by Pashkevich
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Comparison with data

nth 235U (Lang et al.)
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Needed input
Basic ideas of our macroscopic-microscopic
fission approach (Inspired by Smirenkin, Maruhn,
Pashkevich, Rusanov, Itkis, ...) Macroscopic
Potential near saddle from exp. mass
distributions at high E (Rusanov) Macroscopic
potential is property of fissioning system (
f(ZCN2/ACN))
The figure shows the second derivative of the
mass-asymmetry dependent potential, deducedfrom
the widths of the mass distributions withinthe
statistical model compared to different LD model
predictions. Figure from Rusanov et al. (1997)
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Ternary fission
Ternary fission ? less than 1 of a binary
fission
Open symbols - experiment Full symbols - theory
Rubchenya and Yavshits, Z. Phys. A 329 (1988) 217
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Applications in astrophysics - first step
Mass and charge distributions in
neutrino-induced fission of r-process
progenitors ?
Phys. Lett. B616 (2005) 48