role of the fission in the r-process nucleosynthesis - needed input - aleksandra kelić and...

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

- Needed input- Needed input - -Aleksandra Kelić and Karl-Heinz Schmidt

GSI-Darmstadt, Germany

• What is the needed input?• Mass and charge division in fission • Saddle-point masses • Conclusions

r-process and fission r-process and fission

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

Astrophysical conditions? Characteristics of the fission process?

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

Fission process Fission process Fission corresponds to a large-scale collective motion:

Both static (e.g. potential) and dynamic (e.g. viscosity) properties play important role. At low excitation energies: influence of shell effects and pairing correlations.


What do we need?What do we need?

• Fission barriers• Fragment distributions• Level densities (pairing, shell corrections, symmetry classes)• Nuclear viscosity• Particle-emission widths

Fission competition in de-excitation of excited nuclei

E*


Source of informationSource of information

2028

50

82

82

50

2820

82

- No experimental information- Relay on theory and model calculationsAleksandra KeliAleksandra Kelić (GSI)ć (GSI) NPA3 – Dresden, 30.03.2007 NPA3 – Dresden, 30.03.2007

Estimated beam intensities at the Estimated beam intensities at the future FAIR facility (K.-H. Schmidt et al)future FAIR facility (K.-H. Schmidt et al)

Mass and charge division in fissionMass and charge division in fission

Experimental information - Low energyExperimental information - Low energy

• Particle-induced fission of long-lived targets and spontaneous fission:- A(E*) in most cases- A and Z distributions of light fission group only in the thermal-neutron induced fission on the stable targets

• EM fission of secondary beams at GSI:- Z distributions at "one" energy


Basic ideaBasic idea

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

Experimental survey at GSI by use of secondary beams

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


Basic assumptions Basic assumptions Macroscopic part: Given by properties of fissioning nucleus• Potential near saddle from exp. mass distributions at high E* (1): 2

AA

Tc

(1) Rusanov et al, Phys. At. Nucl. 60 (1997) 683 N 82N 88

Microscopic part: Shells near outer saddle "resemble" shells of final fragments (but weaker) (2)

• Properties of shells from exp. nuclide distributions at low E*Dynamics: Approximations based on Langevin calculations (3):• Mass asymmetry: decision near outer saddle• N/Z: decision near scission

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

(2) Maruhn and Greiner, PRL 32 (1974) 548; Pashkevich, NPA 477 (1988) 1;(3) P. Nadtochy, private communiation


Pashkevich et al.Pashkevich et al.

Macroscopic-microscopic approachMacroscopic-microscopic approach

For each fission fragment we get:• Mass • Nuclear charge• Kinetic energy• Excitation energy• Number of emitted particles

Model parameters:• Curvatures, strengths and positions of two microscopic contributions as free parameters • These 6 parameters are deduced from the experimental fragment distributions and kept fixed for all systems and energies.

N 82 N 88Aleksandra 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 - experimentred - calculations

With one and same With one and same set of model set of model parameters for all parameters for all systemssystems


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

Applications in astrophysicsApplications in astrophysics

260U 276Fm 300U

Usually one assumes:a) symmetric split: AF1 = AF2

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

Be careful:

Deatailed r-process network calculations: Deatailed r-process network calculations: N. Zinner (Aarhus) and N. Zinner (Aarhus) and G. Martinez-Pinedo (GSI)G. Martinez-Pinedo (GSI)


Saddle-point massesSaddle-point masses

Fission barriers - Experimental informationFission barriers - Experimental information

Relative uncertainty:

>10-2

Available data on fission barriers, Z ≥ 80 (RIPL-2 library)


Fission barriers - Experimental informationFission barriers - Experimental information

Fission barriersRelative uncertainty:

>10-2

GS massesRelative uncertainty:

10-4 - 10-9

Courtesy of C. Scheidenberger (GSI)Aleksandra KeliAleksandra Kelić (GSI)ć (GSI) NPA3 – Dresden, 30.03.2007 NPA3 – Dresden, 30.03.2007

Open problemOpen problem Limited experimental information on the height of the fission barrier

Neutron-induced fission rates for U isotopes

Panov et al., NPA 747 (2005)Aleksandra KeliAleksandra Kelić (GSI)ć (GSI) NPA3 – Dresden, 30.03.2007 NPA3 – Dresden, 30.03.2007

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

Usad Empirical saddle-point shell-correction energy

)(expexp macrof

macroGSGSfsad EMMEU

Macroscopic saddle-point

mass

Experimental saddle-point

mass


IdeaIdea

If an model is realistic Slope of Usad as function of N should be ~ 0Any general trend would indicate shortcomings of the macroscopic model.

SCE

Neutron number

Very

schematic!

What do we know about saddle-point shell-correction energy?1. Shell corrections have local character2. Shell-correction energy at SP should be very small (e.g Myers and Swiatecki PRC 60 (1999); Siwek-Wilczynska and Skwira, PRC 72 (2005))

1-2 MeV


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


Example for uraniumExample for uranium

Usad as a function of a neutron number

A realistic macroscopic model should give a zero slope!Kelić and Schmidt, PLB 643 (2006)


ResultsResultsSlopes of δUsad as a function of the neutron excess

The most realistic macroscopic models: 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)Aleksandra KeliAleksandra Kelić (GSI)ć (GSI) NPA3 – Dresden, 30.03.2007 NPA3 – Dresden, 30.03.2007

ConclusionsConclusions

- Good description of mass and charge division in fission based on a macroscopic-microscopic approach, which allows for robust extrapolations. Inclusion in r-process network calculations by N. Zinner (Aarhus) and G. Martinez-Pinedo (GSI).

- According to a detailed analysis of the isotopic trends of saddle-point masses indications have been found that the Thomas-Fermi model and the FRLDM model give the most realistic extrapolations in regions where no experimental data are available.

- Need for more precise and new experimental data using new techniques and methods basis for further developments in theory.


Additional slidesAdditional slides

Macroscopic-microscopic approachMacroscopic-microscopic approach- 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;

Macroscopic part: property of CNMicroscopic part: properties of fragments*

N82

N90

Comparison with data - spontaneous fissionComparison with data - spontaneous fission

ExperimentExperiment

CalculationsCalculations(experimental resolution not included)

Comparison with dataComparison with data

nth + 235U (Lang et al.)

Z

Mass distribution Charge distribution

Experiment - DifficultiesExperiment - Difficulties

•Experimental sources:Energy-dependent fission probabilities

•Extraction of barrier parameters:Requires assumptions on level densities

Gavron et al., PRC13 (1976) 2374

Ternary fission Ternary fission

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

Open symbols - experimentFull 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

role of the fission in the r-process nucleosynthesis - needed input - aleksandra kelić and...

Documents