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

2. 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) S121 4) Rauscher et al, APJ 429 (1994) 49 1) Cowan et al, Phys. Rep. 208 (1991) 267   Astrophysical conditions?   Characteristics of the fission process? Aleksandra Kelić (GSI) NPA3 – Dresden, 30.03.2007

3. 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. Aleksandra Kelić (GSI) NPA3 – Dresden, 30.03.2007

4. 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* Aleksandra Kelić (GSI) NPA3 – Dresden, 30.03.2007

5. Source of information 20 28 50 82 50 28 20 82 - No experimental information - Relay on theory and model calculations Aleksandra Kelić (GSI) NPA3 – Dresden, 30.03.2007 Estimated beam intensities at the future FAIR facility (K.-H. Schmidt et al)

6. Mass and charge division in fission

7. Experimental 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 Aleksandra Kelić (GSI) NPA3 – Dresden, 30.03.2007

8. Basic 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 by macroscopic and microscopic properties of the potential-energy landscape near outer saddle. Aleksandra Kelić (GSI) NPA3 – Dresden, 30.03.2007

9. Basic assumptions Macroscopic part: Given by properties of fissioning nucleus Potential near saddle from exp. mass distributions at high E* (1) : (1) Rusanov et al, Phys. At. Nucl. 60 (1997) 683 N  82 N  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 Aleksandra Kelić (GSI) NPA3 – Dresden, 30.03.2007 Pashkevich et al.

10. Macroscopic-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  82N  88 Aleksandra Kelić (GSI) NPA3 – Dresden, 30.03.2007

11. Comparison with EM data 89 Ac 90 Th 91 Pa 92 U 131 135 134 133 132 136 137 138139 140141 142 Fission of secondary beams after the EM excitation: black - experiment red - calculations With one and same set of model parameters for all systems Aleksandra Kelić (GSI) NPA3 – Dresden, 30.03.2007

12. Neutron-induced fission of 238 U 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

13. Applications in astrophysics 260 U 276 Fm 300 U Usually one assumes: a) symmetric split: A F1 = A F2 b) 132 Sn shell plays a role: A F1 = 132, A F2 = A CN - 132 Be careful: Deatailed r-process network calculations: N. Zinner (Aarhus) and G. Martinez-Pinedo (GSI) Aleksandra Kelić (GSI) NPA3 – Dresden, 30.03.2007

14. Saddle-point masses

15. Fission barriers - Experimental information Relative uncertainty: >10 -2 Available data on fission barriers, Z ≥ 80 (RIPL-2 library) Aleksandra Kelić (GSI) NPA3 – Dresden, 30.03.2007

16. Fission barriers - Experimental information Fission barriers Relative uncertainty: >10 -2 GS masses Relative uncertainty: 10 -4 - 10 -9 Courtesy of C. Scheidenberger (GSI) Aleksandra Kelić (GSI) NPA3 – Dresden, 30.03.2007

17. Open 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 Kelić (GSI) NPA3 – Dresden, 30.03.2007

18. Idea Predictions of theoretical models are examined by means of a detailed analysis of the isotopic trends of saddle-point masses.  U sad  Empirical saddle-point shell- correction energy Macroscopic saddle-point mass Experimental saddle-point mass Aleksandra Kelić (GSI) NPA3 – Dresden, 30.03.2007

19. Idea If an model is realistic  Slope of  U sad as function of N should be ~ 0 Any 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 character 2. 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 Aleksandra Kelić (GSI) NPA3 – Dresden, 30.03.2007

20. 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 Aleksandra Kelić (GSI) NPA3 – Dresden, 30.03.2007

21. Example for uranium  U sad as a function of a neutron number A realistic macroscopic model should give a zero slope! Kelić and Schmidt, PLB 643 (2006) Aleksandra Kelić (GSI) NPA3 – Dresden, 30.03.2007

22. Results Slopes of δU sad 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 Kelić (GSI) NPA3 – Dresden, 30.03.2007

23. Conclusions - 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. Aleksandra Kelić (GSI) NPA3 – Dresden, 30.03.2007

24. Additional slides

25. Macroscopic-microscopic approach - Transition from single-humped to double-humped explained by macroscopic 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 CN Microscopic part: properties of fragments* N  82 N  90

26. Comparison with data - spontaneous fission Experiment Calculations (experimental resolution not included)

27. Comparison with data n th + 235 U (Lang et al.) Z Mass distributionCharge distribution

28. Experiment - Difficulties Experimental sources: Energy-dependent fission probabilities Extraction of barrier parameters: Requires assumptions on level densities Gavron et al., PRC13 (1976) 2374

29. 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

30. Applications in astrophysics - first step Mass and charge distributions in neutrino-induced fission of r-process progenitors  Phys. Lett. B616 (2005) 48