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

1. The role of fission in the r-process nucleosynthesisNeeded 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 209Bi).

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

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

6. 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

7. 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

8. Daughternucleus 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

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. Neutron-induced fission rates for U isotopes Panov et al., NPA 747 (2005) Diverging theoretical predictions Theories reproduce measured barriers but diverge far from stability Kelić and Schmidt, PLB 643 (2006)

15. Experimental saddle-point mass Macroscopic saddle-point mass 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. Usad  Experimental minus macroscopic saddle-point mass (should be shell correction at saddle)

16. Very schematic! SCE Neutron number Nature of shell corrections What 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 ofUsad as function of N should be ~ 0 Any general trend would indicate shortcomings of the model.

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

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

19. 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)

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. 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)

22. 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)

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

24. 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

25. 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?

26. 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.)

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

28. 208Pb 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;

29. 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

30. 92U 91Pa 142 140 141 90Th 138 139 89Ac 132 131 133 134 137 135 136 Comparison with EM data 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. 300U 260U 276Fm Application to astrophysics 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! Predicted mass distributions: A. Kelic et al., PLB 616 (2005) 48

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. Mass distribution Charge distribution Z Comparison with data nth + 235U (Lang et al.)

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(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)

38. 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

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