1. W. Udo Schröder, 2007 Spontaneous Fission 1

2. W. Udo Schröder, 2007 Spontaneous Fission 2 Liquid-Drop Oscillations Bohr&Mottelson II, Ch. 6 Surface & Coulomb energies important: Stability limit C  0

3. W. Udo Schröder, 2007 Spontaneous Fission 3 Fissility Mostly considered: small quadrupole and hexadecapole deformations     ≠0 ≠  4 = 40 But 3 =0 (odd electrostatic moment forbidden) Bohr-Wheeler fissility parameter Stability if x < 1

4. W. Udo Schröder, 2007 Spontaneous Fission 4 Fission Potential Energy Surface Fission path   PES Cut along fission path CN Saddle FF 1 FF 2 2m F c 2 m CN c 2 Q Typical fission process:

5. W. Udo Schröder, 2007 Spontaneous Fission 5 LDM-Fission Saddle Shapes Cohen & Swiatecki, 1974

6. W. Udo Schröder, 2007 Spontaneous Fission 6 Systematics of Fission Total Kinetic Energies Viola, Kwiatkowski & Walker, PRC31, 1550 (1985) Average total kinetic energy of both fission fragments as function of fissioning compound nucleus (CN) Z and A:

7. W. Udo Schröder, 2007 Spontaneous Fission 7 Viscosity in Fission For high fissilities (elongated scission shapes) kinetic energies smaller than calculated from saddle Coulomb repulsion: TKE < T f (∞)  viscous energy dissipation. Nix/Swiatecki : Wall and window formula (nucleon transfer, wall motion) Davies et al. PRC13, 2385 (1976) Viscosity 25% of strength in HI collisions FF 1 FF 2 r

8. W. Udo Schröder, 2007 Spontaneous Fission 8 Kramers’ Stochastic Fission Model  V() saddle point P(t)  time  Collective d.o.f.  coupled weakly to internal (nucleonic) d.o.f. Gradual spreading of probability distribution over barrier (saddle). Probability current from j F =0 to stationary value at t  ∞ Grange & Weidenmüller, 1986  trans

9. W. Udo Schröder, 2007 Spontaneous Fission 9 Fission Transient and Delay Times Concepts revisited by H. Hofmann, 2005/2006 Statistical Model fission life time: Level Density V() Inverted parabola Oscill frequ.  sad

10. W. Udo Schröder, 2007 Spontaneous Fission 10 Prescission Neutron Emission D. Hinde et al., PRC45, 1229 (1992) Exptl. setup detects FF, lcps, and n in coincidence  decompose angular distributions Sources CN, FF1, FF2 Systematics: WUS et al.  Berlin Fission Conf. 1988 Short fission times for high E*> 300-500 MeV ?

11. W. Udo Schröder, 2007 Spontaneous Fission 11 Fission Fragment Mass Distributions H. Schmitt et al., PR 141, 1146 (1966) E* Dependence of FF Mass Distribution: asymm  symm n (A) Neutron emission in fission: ≈ 2.5±0.1 232 Th(p, f) E p = Croall et al., NPA 125, 402 (1969) yield n (A) FF Mass A Pre-neutron emission Post-neutron emission Radio-chemical data

12. W. Udo Schröder, 2007 Spontaneous Fission 12 Fission Fragment Z Distributions yield Vandenbosch & Huizenga, 1973 Z p : The most probable Z Same Gaussian A(Z-Z p ) A CN Bimodal mass distributions: With increasing A CN more symmetric. ≈ 1 39 shell stabilized via ≈ 50

13. W. Udo Schröder, 2007 Spontaneous Fission 13 Models for Isobaric Charge Distributions R sc Minimum Potential Energy (MPE) Models App. correct for asymmetric fission (Z ≈ +0.5). Incorrect: o-e effects, trends Z ≈ -0.5 at symmetry. Unchanged charge distribution (UCD): Experimentally not observed, but MPE variance: expand V around Z=Zp: V P(Z) Z

14. W. Udo Schröder, 2007 Spontaneous Fission 14 Models for Isobaric Charge Distributions R sc Try thermal equilibrium (T): Linear increase of  2 with T not observed, but ≈ const. up to E*<50MeV N Z V(Z,N) P(Z,N) A A=const. Studied in heavy-ion reactions.  dynamics? NEM ?

15. W. Udo Schröder, 2007 Spontaneous Fission 15 Mass-Energy Correlations light heavy FF mass ratio Pleasanton et al., PR174, 1500 (1968) 235 U +n th Fission Energies 235 U +n th E F1 -E F2 Correlation Pulse heights in detectors  affected by pulse height defect asymmetric fission: p conservation TKE

16. W. Udo Schröder, 2007 Spontaneous Fission 16 Fine Structure in Fission Excitation Functions J. Blons et al., NPA 477, 231 (1988) match to incoming wave III Also:  and n decay from II class states Class I and II vibrational states coupled

17. W. Udo Schröder, 2007 Spontaneous Fission 17 Shell Effects in Fission LDM barrier only approximate, failed to account for fission isomers, structure details of  f. Shell effects for deformation  Nilsson s.p. levels  accuracy problem  Strutinsky Shell Corr. In some cases: more than 2 minima, different 1., 2., 3. barriers

18. W. Udo Schröder, 2007 Spontaneous Fission 18 Angular Distribution of Symmetry Axis