1. The role of fission in the r-process nucleosynthesis Needed input Aleksandra Kelić and Karl-Heinz Schmidt GSI-Darmstadt, Germany http://www.gsi.de/charms/

2. 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.

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

4. Identifying r-process nuclei 176 Yb, 186 W, 187 Re can only be produced by r-process. Truran 1973

5. Nuclear abundances Characteristic differences in s- and r-process abundances. s-process r-process Cameron 1982

6. Role 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) S121 4) Rauscher et al, APJ 429 (1994) 49 1) Cowan et al, Phys. Rep. 208 (1991) 267

7. Difficulties near A = 120 Are the higher yields around A = 120 an indications for fission cycling? Chen et al. 1995 Calculation with shell quenching (no fission). r-process abundances compared with model calculations (no fission).

8. Relevant features of fission Fission occurs after neutron capture after beta decay Fission competition in de-excitation of excited nuclei Daughter nucleus Most important input: Height of fission barriers Fragment distributions n f γ

9. Saddle-point masses

10. 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

11. Fission barriers - Experimental information Uncertainty: ≈ 0.5 MeV Available data on fission barriers, Z ≥ 80 (RIPL-2 library) Far away from r-process path!

12. 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

13. 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

14. Diverging 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)

15. Idea: 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.  U sad  Experimental minus macroscopic saddle-point mass (should be shell correction at saddle) Macroscopic saddle-point mass Experimental saddle-point mass

16. Nature of shell corrections If a model is realistic  Slope of  U sad 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

17. 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! Topographic theorem: Shell corrections alter the saddle-point mass "only little". (Myers and Swiatecki PRC60, 1999) 238 U

18. Example for uranium  U sad as a function of a neutron number A realistic macroscopic model should give almost a zero slope!

19. Results Slopes of δU sad 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)

20. Mass and charge division in fission - Available experimental information - Model descriptions - GSI model

21. Experimental 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 of potential in mass asymmetry deduced from fission-fragment mass distributions. T/(d 2 V/dη 2 ) σ A 2 ~ T/(d 2 V/dη 2 )

22. Experimental information – low energy Particle-induced fission of long-lived targets and spontaneous fission Available information: - A(E*) in most cases - A and Z distributions of light fission group only in the thermal-neutron induced fission on stable targets EM fission of secondary beams at GSI Available information: - Z distributions at energy of GDR (E*≈12 MeV)

23. Experimental information – low energy K.-H. Schmidt et al., NPA 665 (2000) 221 Experimental survey at GSI by use of secondary beams

24. Models 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

25. Macroscopic-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 dynamics?

26. Most relevant features of the fission process Macroscopic potential: Macroscopic potential is property of fissioning system ( ≈ f(Z CN 2 /A CN )) Potential near saddle from exp. mass distributions at high E* (Rusanov) Microscopic potential: Microscopic corrections are properties of fragments (= f(N f,Z f )). (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 saddle τ (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)

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

28. Test case: multi-modal fission around 226 Th - 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; N≈90 N=82 208 Pb 238 U Macroscopic part: property of CN Microscopic part: properties of fragments* (deduced from data)

29. 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

30. 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

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

32. Application to 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 But! Deformed shell around A≈140 (N≈90) plays an important role! A. Kelic et al., PLB 616 (2005) 48 Predicted mass distributions:

33. 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.

34. 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

35. Additional slides

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

37. 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(Z CN 2 /A CN )) The figure shows the second derivative of the mass-asymmetry dependent potential, deduced from the widths of the mass distributions within the statistical model compared to different LD model predictions. Figure from Rusanov et al. (1997)

38. 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

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