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