Experimental knowledge on nuclear fission analyzed with a semiempirical ordering scheme

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Experimental knowledge on nuclear
fissionanalyzed with a semi-empirical ordering
scheme

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

Supported by the European Union withinHINDAS,
EUROTRANS, EURISOL_DS
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Overview

• Brief overview on fission experiments
• Available information on mass and element
  distributions of fission fragments
• How can we classify measured data?

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Different 'faces' of the fission process
3?Af MeV
Multifragmentation ? 'end' of fission
Transient effects
150 MeV
High-energy fission À la liquid drop
Dissipative phenomena
Excitation energy
Symmetric fission
40 MeV
Low-energy fission Nuclear-structure effects
Dissipation in a superfluid Fermionic system
Bf
Resonance phenomena
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Spontaneous fission
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Mechanisms to induce fission
- Neutron-induced fission (e.g. ILL Grenoble,
IRMM, Jyväskylä, Los Alamos, nTOF...) - Particle
(p, anti-p, p, m) induced fission (e.g.
Jyväskylä, PNPI, GSI, CERN ...) - Photofission
(e.g. CEA, Kurchatov institute, IPNO, GSI,
CERN...) - Transfer and deep-inelastic reactions
(e.g. Los Alamos, Grenoble, IPNO, GANIL ...) -
Heavy-ion induced fission (e.g. Canberra, KVI,
IPHC, GSI...)
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Observables
Large variety of observables
- Fission cross sections - Pre-scission particle
and g multiplicities - Angular anisotropies -
Mass distribution of fragments - Charge
distribution of fragments - Spin distribution of
fragments - Post-scission particle and g
multiplicities - TKE - ...
- Different observables "determined" at different
moments along the fission process ? enables
probing of different stages of fission process
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Experimental difficulties

• - Restricted choice of systems
• Available targets ? stable or long-lived nuclei
• Secondary beams ? no beams above 238U by
  fragmentation
• Reaction products ? limited N/Z range in
  heavy-ion fusion
• - Physical limits on resolution
• Z and A resolution difficult at low energies
• Scattering in target/detector at low energies
  (tails in A/TKE distribution)
• - Restriction to specific mechanisms to induce
  fission in available
• installations
• Lohengrin only thermal neutrons
• FRS only Coulomb fission or fragmentation-fissio
  n reactions
• Fusion high E and spin or spontaneous fission
• - Technical limits on correlations (limitations
  of available installations)
• FRS detects only fission fragments at zero
  degree, no neutrons, no g
• No experimental information available on A and Z
  of both fission fragments

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Overview on available mass and element
distributions of fission fragments
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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 T. Enqvist et al, NPA 686
(2001) 481 (see www.gsi.de/charms/)
Large systematic on sA by Rusanov et al, Phys.
At. Nucl. 60 (1997) 683
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Experimental information Low-energy fission

• Particle-induced fission of long-lived targets
  andspontaneous fission
• Available information
• - A(E) in most cases
• - A and Z distributions of lightfission group
  only in thethermal-neutron induced fissionon
  stable targets
• EM fission of secondary beams at GSI
• Available information
• - Z distributions at energy of GDR (E 11 MeV)

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Experimental information Low-energy fission
Mass TKE distributions usually fitted in the
frame of three fission modes (superlong, standard
1, standard 2)
n(1.7 MeV) 238U
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Classification
Macro-microscopic approach exploiting the
separation of compound nucleus and fragment
properties on the fission path. Basic concept
Yields proportional to available states on the
fission path.
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Assumption 1 Statistical model
- Mass / element yield is proportional to the
available phase space
- At which point one should apply statistical
model to calculate mass distributions? Langevin
calculations ? Somewhere between saddle and
scission. Addev et al, NPA 502, p.405c, T.
Asano et al, JNRS 7, p.7
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Assumption 2 - Preformation hypothesis
U. Mosel and H. W. Schmitt, NPA 165 (1971) 73
By analyzing the single-particle states along
the fission path .. we have established the fact
that the influence of fragment shells reaches far
into the PES. The preformation of the fragments
is almost completed already at a point where the
nuclear shape is necked in only to 40 .
Potential-energy surface of 224Th calculated by
Pashkevich.
Conclusion Shells on the fission path are a
function of N and Z of the fragments!
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What to do?

• ? Use statistical model to correlate measured
  mass / element
• distributions with nuclear potential
• ? Apply statistical model close beyond the outer
  saddle
• ? Mass-asymmetric nuclear potential is given by
  two contributions
• Macroscopic given by the properties of the
  fissioning system
• Microscopic given by the properties of fission
  fragments

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Macroscopic potential - experimental systematics
Experiment In cases when shell effects can be
disregarded (high E), the fission-fragment mass
distribution of heavy systems is Gaussian.
Second derivative of potential in mass asymmetry
deduced from width of fission-fragment mass
distributions.
sA2 T/(d2V/d?2)
? Mulgin et al. NPA 640 (1998) 375
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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Microscopic features

Measured element yields K.-H. Schmidt et al., NPA
665 (2000) 221
Potential-energy landscape (Pashkevich)
Extension of the statistical model to multimodal
fission Yields of fission channels number of
states in the fission valleys
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Microscopic potential deduced from A distribution
M. G. Itkis et al., Sov. J. Nucl. Phys. 43
(1986) 719
Input - Experimental yields and -
Macroscopic yields
Result - Shell-correction energy
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Microscopic potential deduced from A distribution
M. G. Itkis et al., Sov. J. Nucl. Phys. 43
(1986) 719
Symbols - "experimental" shell corrections Line
theoretical shell correction (A.V. Pashkevich)
Conclusion Shell corrections have universal
character.
Limited to only few systems, and shell
corrections considered in mass only
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Microscopic potential of other systems
? Parameters used to deduce microscopic
contribution
Shape of microscopic potential varies drastically.
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Shells of fragments
Importance of spherical and deformed neutron
shells
Wilkins et al. PRC 14 (1976) 1832
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Test case fission modes from 226Th to 260Md
Simplified illustrationSchematic decomposition
of microscopic structure by N 82 (Standard 1)
and N 92 (Standard 2) shells, only.Same shell
parameters for all cases.
Global features of microscopic structure are
reproduced.
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Test case multi-modal fission around 226Th
These ideas represent the basis of the GSI
semi-empirical fission model. Additional
content - Influence of the proton Z50 shell on
the Standard 1 mode - Decreasing strength of
combined Z50 and N82 shells when going away
from A132 (obtained from GS shell-correction
energy) - Charge polarisation effects - Particle
emission on different stages
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Multimodal fission around 226Th
Black experimental data (GSI experiment)Red
model calculations (N82, Z50, N92 shells)
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Neutron-induced fission of 238U for En 1.2 to
5.8 MeV
Data - F. Vives et al, Nucl. Phys. A662 (2000)
63 Lines Calculations
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Other observables
Spontaneous fission of 252Cf
Mass
Neutrons
TKE
Line Model calculations
Data Hambsch et al, NPA617 Walsh et al,
NPA 276 Zakharova et al, Wahl,
ADNDT 39
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Future
Electron-ion collider ELISE of FAIR project of
GSI, Darmstadt. (Rare-isotope beams tagged
photons) Aim Precise fission data over large N/Z
range.
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Conclusions
- Using a semi-empirical ordering scheme based on
the macro-microscopic approach and the
separability of compound-nucleus and fragment
properties along the fission path a large portion
of common features behind the variety of the
complex observation has been revealed. - While
separate calculations of shell effects or
separate microscopic calculations for the
different fissioning systems suffer from
individual numerical uncertainties attributed to
every single system, the separability principle
suggests that the shell effects are essentially
the same for all fissioning systems. - Good
bases for modelling the fission process.
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Influence of experimental geometry

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Comparison with 238U (1 A GeV) 1H
Full calculation with ABRABLA07 code (description
of fission included) Comparison ofnuclide yields
andmoments. (M. V. Ricciardi et al., PRC 73
(2006) 014607)
ABRABLA07Monte-Carlo code,abrasion,
multifragm.continuous emission of n, LCP, IMF,
fission (transients, Nf,Zf,TKE, evaporation pre,
post)
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Comparison with data - spontaneous fission

Experiment
ABRABLA Calculations (experimental resolution not
included)