Experimental knowledge on Experimental knowledge on nuclear fissionnuclear fissionanalyzed with a analyzed with a

semi-empirical ordering schemesemi-empirical ordering scheme

Karl-Heinz Schmidt, Aleksandra Kelić,

Maria Valentina Ricciardi

GSI-Darmstadt, Germany

http://www.gsi.de/charms/ Supported by the European Union withinSupported by the European Union withinHINDAS, EUROTRANS, EURISOL_DSHINDAS, EUROTRANS, EURISOL_DS

OverviewOverview

• Brief overview on fission experiments

• Available information on mass and element

distributions of fission fragments

• How can we classify measured data?

Different 'faces' of the fission processDifferent 'faces' of the fission processE

xcita

tion

ener

gy

0

~ Bf

~ 40 MeV

~ 150 MeV

~3Af MeV

Low-energy fission

Nuclear-structure effects

High-energy fission

À la liquid drop

Spontaneous fission

Resonance phenomena

Symmetric fission

Dissipative phenomena

Transient effects

Multifragmentation 'end' of fission

Dissipation in a superfluid Fermionic system

Mechanisms to induce fissionMechanisms to induce fission

- Neutron-induced fission

(e.g. ILL Grenoble, IRMM, Jyväskylä, Los Alamos, nTOF...)

- Particle (p, anti-p, , ) 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...)

ObservablesObservables

- Fission cross sections

- Pre-scission particle and multiplicities

- Angular anisotropies

- Mass distribution of fragments

- Charge distribution of fragments

- Spin distribution of fragments

- Post-scission particle and multiplicities

- TKE

- ...

Large variety of observables:

- Different observables "determined" at different moments along the fission process enables probing of different stages of fission process

F

Mpre

Experimental difficultiesExperimental 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 • 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 energyExperimental 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 fissionExperimental 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)

Experimental information – Low-energy fissionExperimental 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:

ClassificationClassification

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 modelAssumption 1 – Statistical model

AUEadEAYAUE

*)(

0

* 2exp,

*

- 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

Exp data measured at GSI

Assumption 2 - Preformation hypothesisAssumption 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 %.“

Conclusion: Shells on the fission path are a function of N and Z of the fragments!!

Potential-energy surface of Potential-energy surface of 224224Th Th calculated by Pashkevichcalculated by Pashkevich..

What to do?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 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.

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)

← Mulgin et al. NPA 640 (1998) 375

Second derivative of potential in mass asymmetry deduced from width of fission-fragment mass distributions.

σA2 ~ T/(d2V/dη2)

Microscopic featuresMicroscopic features

Potential-energy landscape (Pashkevich)

Measured element yields

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 Microscopic potential deduced from AA distribution distribution

Input: - Experimental yields and - „Macroscopic“ yields

Result: - Shell-correction energy

M. G. Itkis et al., Sov. J. Nucl. Phys. 43 (1986) 719

effT

U

Y

Y exp

macro

exp

Microscopic potential deduced from Microscopic potential deduced from AA distribution distribution

M. G. Itkis et al., Sov. J. Nucl. Phys. 43 (1986) 719

Conclusion: Shell corrections have “universal” character.

Symbols - "experimental" shell correctionsLine – theoretical shell correction (A.V. Pashkevich)

Limited to only few systems, and shell corrections considered in mass only

Microscopic potential of other systemsMicroscopic potential of other systems

Shape of microscopic potential varies drastically.

System A(macroscopic) Teff

226Th (E* ≈ 11 MeV) 8.8 0.6 MeV

238U(n,f), En = 1.7 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

Shells of fragmentsShells of fragments

Importance of spherical and deformed neutron shells

Wilkins et al. PRC 14 (1976) 1832

Test case: fission modes from Test case: fission modes from 226226Th to Th to 260260MdMd

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.

Global features of microscopic structure are reproduced..

Shell Depth Width (σA)

N = 82 -3.3 MeV 3.5

N = 92 -4.0 MeV 7.0

Test case: multi-modal fission around Test case: multi-modal fission around 226226ThTh

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 Multimodal fission around 226226ThTh

Black: experimental data (GSI experiment)Red: model calculations (N=82, Z=50, N=92 shells)

89Ac

90Th

91Pa

92U

131

135

134

133

132

136

137

138

139

140

141

142

Neutron-induced fission of Neutron-induced fission of 238238U for U for EEnn = 1.2 to 5.8 MeV = 1.2 to 5.8 MeV

Data - F. Vives et al, Nucl. Phys. A662 (2000) 63; Lines – Calculations

Other observablesOther observables

Spontaneous fission of 252Cf

Mass: Neutrons: TKE:

Data:

Hambsch et al, NPA617 Walsh et al, NPA 276 Zakharova et al,

Wahl, ADNDT 39

Line: Model calculations

FutureFuture

Electron-ion collider ELISE of FAIR project of GSI, Darmstadt.

(Rare-isotope beams + tagged photons)

Aim: Precise fission data over large N/Z range.

ConclusionsConclusions

- 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.

Influence of experimental geometryInfluence of experimental geometry

Comparison with Comparison with 238238U (1 A GeV) + U (1 A GeV) + 11HH

Full calculation with ABRABLA07 code (description of fission included)

Comparison ofnuclide yields andmoments.

(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 fissionComparison with data - spontaneous fission

Experiment

ABRABLA Calculations

(experimental resolution not included)