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Nuclear Fission

Nuclear Fission. Liquid-Drop Oscillations. Bohr&Mottelson II, Ch. 6. Surface & Coulomb energies important: Stability limit C l  0. Fissility. Mostly considered: small quadrupole and hexadecapole deformations b 2 =a 20 ≠0 ≠ b 4 = a 40 But b 3 = 0 (odd electrostatic moment forbidden).

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Nuclear Fission

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  1. Nuclear Fission Spontaneous Fission

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

  3. Fissility Mostly considered: small quadrupole and hexadecapole deformations b2=a20≠0 ≠ b4=a40 But b3=0 (odd electrostatic moment forbidden) Bohr-Wheeler fissility parameter Stability if x < 1 Spontaneous Fission

  4. b4 PES b2 Cut along fission path Fission Potential Energy Surface Fission path Q Saddle CN Spontaneous Fission mCNc2 FF1 FF2 2mFc2 Typical fission process:

  5. LDM-Fission Saddle Shapes Spontaneous Fission Cohen & Swiatecki, 1974

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

  7. FF1 FF2 r Viscosity in Fission For high fissilities (elongated scission shapes) kinetic energies smaller than calculated from saddle Coulomb repulsion: TKE < Tf (∞)  viscous energy dissipation. Nix/Swiatecki : Wall and window formula (nucleon transfer, wall motion) Spontaneous Fission Viscosity 25% of strength in HI collisions Davies et al. PRC13, 2385 (1976)

  8. P(b,t) time  b V(b) saddle point Kramers’ Stochastic Fission Model Grange & Weidenmüller, 1986 Collective d.o.f. (b) coupled weakly to internal (nucleonic) d.o.f. ttrans Spontaneous Fission b Gradual spreading of probability distribution over barrier (saddle). Probability current from jF =0 to stationary value at t  ∞

  9. V(b) Inverted parabolaOscill frequ. wsad Fission Transient and Delay Times Statistical Model fission life time: Level Density Spontaneous Fission Concepts revisited by H. Hofmann, 2005/2006

  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 Spontaneous Fission Short fission times for high E*> 300-500 MeV ? Systematics: WUS et al.  Berlin Fission Conf. 1988

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

  12. yield <Alight> <Aheavy> ACN Fission Fragment Z Distributions Vandenbosch & Huizenga, 1973 Bimodal mass distributions: With increasing ACN more symmetric. <Aheavy> ≈ 139 shell stabilized via <Zheavy>≈ 50 Spontaneous Fission Zp: The most probable Z Same Gaussian A(Z-Zp)

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

  14. Rsc A Z V(Z,N) P(Z,N) A=const. N Models for Isobaric Charge Distributions Try thermal equilibrium (T): Linear increase of s2 with T not observed, but s≈ const. up to E*<50MeV Spontaneous Fission  dynamics? NEM ? Studied in heavy-ion reactions.

  15. TKE TKE Mass-Energy Correlations Pleasanton et al., PR174, 1500 (1968) asymmetric fission: p conservation 235U +nth Fission Energies 235U +nth EF1-EF2 Correlation FF mass ratio Spontaneous Fission heavy light Pulse heights in detectors  affected by pulse height defect

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

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

  18. Angular Distribution of Symmetry Axis Spontaneous Fission

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