Transcript Document

Experimental knowledge on
nuclear fission
analyzed with a
semi-empirical ordering scheme
Karl-Heinz Schmidt, Aleksandra Kelić,
Maria Valentina Ricciardi
GSI-Darmstadt, Germany
http://www.gsi.de/charms/
Supported by the European Union within
HINDAS, EUROTRANS, EURISOL_DS
Overview
•
Brief overview on fission experiments
•
Available information on mass and element
distributions of fission fragments
•
How can we classify measured data?
Excitation energy
Different 'faces' of the fission process
~3Af MeV
Multifragmentation  'end' of fission
~ 150 MeV
Transient effects
Dissipative phenomena
High-energy fission
À la liquid drop
Symmetric fission
~ 40 MeV
Dissipation in a superfluid
Fermionic system
~ Bf
0
Resonance phenomena
Spontaneous fission
Low-energy fission
Nuclear-structure
effects
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...)
Observables
Large variety of observables:
- Fission cross sections
- Pre-scission particle and g multiplicities
- Angular anisotropies
Mpre
F
- 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
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-fission 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
simultaneously
Overview on available mass and element
distributions of fission fragments
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 A by Rusanov et al, Phys. At. Nucl. 60 (1997) 683
Experimental information – Low-energy fission
• 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 stable targets
• EM fission of secondary beams at GSI
Available information:
- Z distributions at energy of GDR (E* ≈ 11 MeV)
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:
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.
Assumption 1 – Statistical model
- Mass / element yield is proportional to the available phase space :


Y A, E * 
E * U ( A )

*





d


exp
2
a
E
 U  A


0
Exp data measured at GSI
- 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
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!
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
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 fissionfragment mass
distributions.
σA2 ~ T/(d2V/dη2)
← 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)
Microscopic features
Measured element yields
Potential-energy landscape (Pashkevich)
K.-H. Schmidt et al., NPA 665 (2000) 221
Extension of the statistical model to multimodal fission:
Yields of fission channels ~ number of states in the fission valleys
Microscopic potential deduced from A distribution
M. G. Itkis et al., Sov. J. Nucl. Phys. 43 (1986) 719
Input:
- Experimental yields and
- „Macroscopic“ yields
Yexp
Ymacro
 U 
 exp 

 Teff 
Result:
- Shell-correction energy
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
Microscopic potential of other systems
System
226Th
(E* ≈ 11 MeV)
238U(n,f),
En = 1.7 MeV
A(macroscopic)
Teff
8.8
0.6 MeV
9.5
0.4 MeV
252Cf
(spont. fission)
11.3
0.6 MeV
260Md
(spont. fission)
12.2
0.6 MeV
 Parameters used to deduce
microscopic contribution
Shape of microscopic potential varies drastically.
Shells of fragments
Importance of spherical and deformed neutron shells
Wilkins et al.
PRC 14 (1976) 1832
Test case: fission modes from 226Th to 260Md
Simplified illustration:
Schematic decomposition of microscopic structure by
N = 82 (Standard 1) and N ≈ 92 (Standard 2) shells, only.
Same shell parameters for all cases. Shell Depth Width (σ )
A
N = 82
-3.3 MeV
3.5
N = 92
-4.0 MeV
7.0
Global features of microscopic structure are reproduced.
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 Z=50 shell on the Standard 1 mode
- Decreasing strength of combined Z=50 and N=82 shells when
going away from A=132 (obtained from GS shell-correction
energy)
- Charge polarisation effects
- Particle emission on different stages
Multimodal fission around 226Th
92U
91Pa
142
140
141
90Th
138
139
89Ac
131
132
133
134
135
136
137
Black: experimental data (GSI experiment)
Red: model calculations (N=82, Z=50, N=92 shells)
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
Other observables
Spontaneous fission of 252Cf
Mass:
Neutrons:
TKE:
Line: Model calculations
Data:
Hambsch et al, NPA617
Walsh et al, NPA 276
Wahl, ADNDT 39
Zakharova et al,
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.
Conclusions
- Using a semi-empirical ordering scheme based on the macromicroscopic 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.
Influence of experimental geometry
Comparison with 238U (1 A GeV) + 1H
Full calculation
with ABRABLA07
code (description
of fission included)
Comparison of
nuclide yields and
moments.
(M. V. Ricciardi et
al., PRC 73 (2006)
014607)
ABRABLA07:
Monte-Carlo code,
abrasion, multifragm.
continuous emission
of n, LCP, IMF, fission
(transients, Nf,Zf,TKE,
evaporation pre, post)
Comparison with data - spontaneous fission
Experiment
ABRABLA
Calculations
(experimental resolution
not included)