The role of fission in the The role of fission in the

r-process r-process nucleosynthesisnucleosynthesis

Needed inputNeeded input

Aleksandra Kelić and Karl-Heinz SchmidtGSI-Darmstadt, Germany

http://www.gsi.de/charms/

OverviewOverview

• Characteristics of the astrophysical r-process

• Signatures of fission in the r-process

• Relevant fission characteristics and their uncertainties

• Benchmark of fission saddle-point masses*

• GSI model on nuclide distribution in fission*

• Conclusions

*) *) Attempts to improve the fission input of r-process Attempts to improve the fission input of r-process calculations.calculations.

NucleosynthesisNucleosynthesis

Only the r-process leads to the heaviest nuclei (beyond 209Bi).

Identifying r-process nucleiIdentifying r-process nuclei

176Yb, 186W, 187Re can only be produced by r-process.

Truran 1973Truran 1973

Nuclear abundancesNuclear abundances

Characteristic differences in s- and r-process abundances.

s-processs-process

r-processr-process

Cameron Cameron 19821982

Role of fission in the r-processRole of fission in the r-process

Cameron 2003

2) Panov et al., NPA 747 (2005) 633

TransU elements ? 1)

Fission cycling ? 3, 4)

r-process endpoint ? 2)

3) Seeger et al, APJ 11 Suppl. (1965) S1214) Rauscher et al, APJ 429 (1994) 49

1) Cowan et al, Phys. Rep. 208 (1991) 267

Difficulties near A = 120Difficulties near A = 120

Are the higher yields around A = 120 an indications for fission cycling?

Chen et al. 1995Chen et al. 1995

Calculation with shell Calculation with shell quenching (no fission).quenching (no fission).

r-process abundances r-process abundances compared with model compared with model calculations (no calculations (no fission).fission).

Relevant features of fissionRelevant features of fission

Fission occurs

• after neutron capture

• after beta decay

Fission competition in de-excitation of excited nuclei

Daughternucleus

Most important input:

• Height of fission barriers

• Fragment distributions

nn ff

γγ

Saddle-point massesSaddle-point masses

Experimental methodExperimental method

• Experimental sources:

Energy-dependent fission probabilities

• Extraction of barrier parameters:

Requires assumptions on level densities

Resulting uncertainties:

about 0.5 to 1 MeV

Gavron et al., PRC13 (1976) 2374

Fission barriers - Experimental informationFission barriers - Experimental information

Uncertainty: ≈ 0.5 MeV

Available data on fission barriers, Z ≥ 80 (RIPL-2 library)Far away from r-process path!

Complexity of potential energy on the fission pathComplexity of potential energy on the fission path

Influence of nuclear structure (shell corrections, pairing, ...)Higher-order deformations are important (mass asymmetry, ...)

LDM

LDM+Shell

Studied modelsStudied models

1.) Droplet model (DM) [Myers 1977], which is a basis of often used results of the Howard-Möller fission-barrier calculations [Howard&Möller 1980]

2.) Finite-range liquid drop model (FRLDM) [Sierk 1986, Möller et al

1995]

3.) Thomas-Fermi model (TF) [Myers&Swiatecki 1996, 1999]

4.) Extended Thomas-Fermi model (ETF) [Mamdouh et al. 2001]

W.D. Myers, „Droplet Model of Atomic Nuclei“, 1977 IFI/PlenumW.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 14606-1A. Mamdouh et al, NPA 679 (2001) 337

Diverging theoretical predictionsDiverging theoretical predictions Theories reproduce measured barriers but diverge far from stability

Neutron-induced fission rates for U isotopes

Panov et al., NPA 747 (2005)Kelić and Schmidt, PLB 643 (2006)

Idea: Refined analysis of isotopic trendIdea: Refined analysis of isotopic trend

Predictions of theoretical models are examined by means of a detailed analysis of the isotopic trends of saddle-point masses.

Usad Experimental minus macroscopic saddle-point mass (should be shell correction at saddle)

)(expexp macrof

macroGSGSfsad EMMEU

Macroscopic saddle-point

mass

Experimental saddle-point

mass

Nature of shell correctionsNature of shell corrections

If a model is realistic Slope of Usad as function of N should be ~ 0

Any general trend would indicate shortcomings of the model.

SCE

Neutron number

Very

schematic

!

What do we know about saddle-point shell-correction energy?

1. Shell corrections have local character

2. Shell-correction energy at SP should be small (topographic theorem: e.g Myers and Swiatecki PRC 60; Siwek-Wilczynska and Skwira, PRC 72)

1-2 MeV

The topographic theoremThe topographic theorem

Detailed and

quantitative

investigation of the

topographic properties

of the potential-energy

landscape (A. Karpov et

al., to be published)

confirms the validity of

the topographic theorem

to about 0.5 MeV!

Topographic theorem: Shell corrections alter the saddle-point mass "only little". (Myers and Swiatecki PRC60, 1999)

238U

Example for uraniumExample for uranium

Usad as a function of a neutron number

A realistic macroscopic model should give almost a zero slope!

ResultsResults

Slopes of δUsad 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

Kelić and Schmidt, PLB 643 (2006)

Mass and charge division in fissionMass and charge division in fission

- - Available experimental informationAvailable experimental information

- Model descriptions- Model descriptions

- GSI model- GSI model

Experimental information - high energyExperimental information - high energy

In cases when shell effects can be disregarded (high E*), the fission-fragment mass distribution 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. 1998

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

σA2 ~ T/(d T/(d22V/dV/dηη22))

Experimental information – low energyExperimental information – low energy

• 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 beamsat GSI

Available information:

- Z distributions at energy of GDR (E*≈12 MeV)

Experimental information – low energyExperimental information – low energy

K.-H. Schmidt et al., NPA 665 (2000) 221

Experimental survey at GSI by use of secondary beams

Models on fission-fragment distributionsModels on fission-fragment distributions

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

GCM:

Empirical systematics on A or Z distributions – Not suited for extrapolations

Semi-empirical models – Our choice: Theory-guided systematics

Theoretical models - Way to go, not always precise enough and still very time consuming

Macroscopic-microscopic approachMacroscopic-microscopic approach

Potential-energy landscape (Pashkevich)

Measured element yields

K.-H. Schmidt et al., NPA 665 (2000) 221

Close relation between potential energy and yields. Role of Close relation between potential energy and yields. Role of dynamics?dynamics?

Most relevant features of the fission processMost relevant features of the fission process

Macroscopic potential: Macroscopic potential is property of fissioning system ( ≈ f(ZCN

2/ACN))Potential near saddle from exp. mass distributions at high E* (Rusanov)Microscopic potential:

Microscopic corrections are properties of fragments (= f(Nf,Zf)). (Mosel)-> Shells near outer saddle "resemble" shells of final fragments.Properties of shells from exp. nuclide distributions at low E*. (Itkis)Main shells are N = 82, Z = 50, N ≈ 90 (Responsible for St. I and St. II)

(Wilkins et al.)

Dynamical features: Approximations based on Langevin calculations (P. Nadtochy)τ (mass asymmetry) >> τ (saddle-scission): Mass frozen near saddleτ (N/Z) << τ (saddle-scission) : Final N/Z decided near scission

Basic ideas of our macro-micro fission approach(Inspired by Smirenkin, Maruhn, Mosel, Pashkevich, Rusanov, Itkis, ...)

Statistical features: Population of available states with statistical weight (near saddle or scission)

Shells of fragmentsShells of fragments

Two-centre shell-model calculation by A. Karpov, 2007 (private communication)

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

- Transition from single-humped to double-humped explained bymacroscopic and microscopic properties of the potential-energy landscape near outer saddle.

* Maruhn and Greiner, Z. Phys. 251 (1972) 431, PRL 32 (1974) 548; Pashkevich, NPA 477 (1988) 1;

N≈90N=82

208Pb 238U

Macroscopic part: property of CNMicroscopic part: properties of fragments* (deduced from data)

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

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

Aleksandra KeliAleksandra Kelić (GSI)ć (GSI) NPA3 – Dresden, 30.03.2007 NPA3 – Dresden, 30.03.2007

Comparison with EM dataComparison with EM data

89Ac

90Th

91Pa

92U

131

135

134

133

132

136

137

138

139

140

141

142

Fission of secondary beams after the EM excitation:

black - experiment

red - calculations

Comparison with data - spontaneous fissionComparison with data - spontaneous fission

ExperimentExperiment

CalculationsCalculations(experimental resolution not included)

Application to astrophysicsApplication to astrophysics

260U 276Fm 300U

Usually one assumes:

a) symmetric split: AF1 = AF2

b) 132Sn shell plays a role: AF1 = 132, AF2 = ACN - 132

But! Deformed shell around A≈140 (N≈90) plays an important role!

A. Kelic et al., PLB 616 (2005) 48A. Kelic et al., PLB 616 (2005) 48

Predicted mass distributions:

A new experimental approach to fissionA new experimental approach to fission

Electron-ion collider ELISE of FAIR project.

(Rare-isotope beams + tagged photons)

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

ConclusionsConclusions

- Important role of fission in the astrophysical r-process End point in production of heavy masses, U-Th

chronometer. Modified abundances by fission cycling.

- Needed input for astrophysical network calculationsFission barriers.Mass and charge division in fission.

- Benchmark of theoretical saddle-point massesInvestigation of the topographic theorem.Validation of Thomas-Fermi model and FRLDM model.

- Development of a semi-empirical model for mass and charge division in fission

Statistical macroscopic-microscopic approach. with schematic dynamical features and empirical input.

Allows for robust extrapolations.

- Planned net-work calculations with improved input (Langanke et al)

- Extended data base by new experimental installations

Additional slidesAdditional slides

Comparison with dataComparison with data

nth + 235U (Lang et al.)

Z

Mass distribution Charge distribution

Needed input 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(ZCN

2/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)

Ternary fission Ternary fission

Rubchenya and Yavshits, Z. Phys. A 329 (1988) 217

Open symbols - experiment

Full symbols - theory

Ternary fission less than 1% of a binary fission

Applications in astrophysics - first stepApplications in astrophysics - first step

Mass and charge distributions in neutrino-induced fission of

r-process progenitors

Phys. Lett. B616 (2005) 48