1 / 18

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).

zeke
Download Presentation

Nuclear Fission

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related