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The role of fission in the r-process nucleosynthesis Needed input

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### The role of fission in the r-process nucleosynthesisNeeded input

Aleksandra Kelić and Karl-Heinz Schmidt

GSI-Darmstadt, Germany

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

Overview

- 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 calculations.

Nucleosynthesis

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

Nuclear abundances

Characteristic differences in s- and r-process abundances.

r-process

s-process

Cameron 1982

Role of fission in the r-process

TransU elements ? 1)

r-process endpoint ? 2)

Fission cycling ? 3, 4)

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

Cameron 2003

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

3) Seeger et al, APJ 11 Suppl. (1965) S121

4) Rauscher et al, APJ 429 (1994) 49

Difficulties near A = 120

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

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

Calculation with shell quenching (no fission).

Chen et al. 1995

Relevant features of fission

Fission competition in de-excitation of excited nuclei

f

n

γ

- Fission occurs
- after neutron capture
- • after beta decay

- Most important input:
- Height of fission barriers
- • Fragment distributions

Experimental 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 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 path

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

LDM

LDM+Shell

Studied 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/Plenum

W.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 14606-1

A. Mamdouh et al, NPA 679 (2001) 337

Neutron-induced fission rates for U isotopes

Panov et al., NPA 747 (2005)

Diverging theoretical predictionsTheories reproduce measured barriers but diverge far from stability

Kelić and Schmidt, PLB 643 (2006)

Experimental saddle-point mass

Macroscopic saddle-point mass

Idea: Refined analysis of isotopic trendPredictions 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)

SCE

Neutron number

Nature of shell correctionsWhat do we know about saddle-point shell-correction energy?

1. Shell corrections have local character

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

1-2 MeV

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

Any general trend would indicate shortcomings of the model.

The 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!

238U

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

Example for uranium

Usadas a function of a neutron number

A realistic macroscopic model should give almost a zero slope!

Results

Slopes of δUsadas a function of the neutron excess

Themost 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 fission

- Available experimental information

- Model descriptions

- GSI model

Experimental information - high energy

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

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

σA2~ T/(d2V/dη2)

← Mulgin et al. 1998

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)

Experimental 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 energy

Experimental survey at GSI by use of secondary beams

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

Models on fission-fragment distributions

Empirical systematicson A or Z distributions – Not suited for extrapolations

Theoretical models - Way to go, not always precise enough and

still very time consuming

Encouraging progress in a full microscopic description of fission:

H. Goutte et al., PRC 71 (2005) Time-dependent HF calculations with GCM:

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

Macroscopic-microscopic approach

Measured element yields

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

Potential-energy landscape (Pashkevich)

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

Most relevant features of the fission process

Basic ideas of our macro-micro fission approach

(Inspired by Smirenkin, Maruhn, Mosel, Pashkevich, Rusanov, Itkis, ...)

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

Statistical features:

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

Macroscopic potential:

Macroscopic potential is property of fissioning system ( ≈ f(ZCN2/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.)

Shells of fragments

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

238U

N≈90

N=82

Test case: multi-modal fission around 226Th- Transition from single-humped to double-humped explained by

macroscopic and microscopic properties of the potential-energy landscape near outer saddle.

Macroscopic part: property of CN

Microscopic part: properties of fragments* (deduced from data)

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

Neutron-induced fission of 238U for En = 1.2 to 5.8 MeV

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

Aleksandra Kelić (GSI) NPA3 – Dresden, 30.03.2007

91Pa

142

140

141

90Th

138

139

89Ac

132

131

133

134

137

135

136

Comparison with EM dataFission of secondary beams after the EM excitation:

black - experiment

red - calculations

Comparison with data - spontaneous fission

Experiment

Calculations

(experimental resolution not included)

260U

276Fm

Application to astrophysicsUsually 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!

Predicted mass distributions:

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

A 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.

Conclusions

- 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 calculations Fission barriers. Mass and charge division in fission.

- Benchmark of theoretical saddle-point masses Investigation 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

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(ZCN2/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 less than 1% of a binary fission

Open symbols - experiment

Full symbols - theory

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

Applications in astrophysics - first step

Mass and charge distributions in neutrino-induced fission of

r-process progenitors

Phys. Lett. B616 (2005) 48

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