Comparison of Rotating Finite Range Model and Thomas-Fermi Fission barriers

1. Comparison of Rotating Finite Range Model and Thomas-Fermi Fission barriers K. Mahata Nuclear Physics Division Bhabha Atomic Research Centre Mumbai –400 085, INDIA

2. Plan of the talk • Introduction • Fission barrier models • Compound nucleus formation and decay • Statistical model of CN decay • Discrepancy in fold distribution measurement • Inconsistency in fold distribution and cross-section • Summary an conclusion

3. Energy Bf Introduction • Fission barrier which inhibit fission results from near cancellation of surface and Coulomb energy. • Single particle effects • Angular momentum dependence • Compound nucleus formation • Competition between the fission and the particle evaporation channel • saddle point shape determine the angular distribution of fission fragments.

4. Fission barrier model • Rotating Liquid Drop Model (1974): • Potential energies and equilibrium configuration of a rotating uniformly charged incompressible fluid with sharp boundary. • Bf required to reduce by a factor varying between 0.5 to 0.9 • extractedeff were found to be larger. • Rotating Finite Range Model (1986): • Finite range effects in the nuclear surface energy • Finite surface diffuseness effects in the Coulomb energy and effective moment of inertia. • Thomas-Fermi Model (1996): • Effective two-body interaction were adjusted to fit shell-corrected masses, diffuseness of nuclear surface and depth of optical model potential

5. Angular momentum dependence Thomas-Fermi fission barrier falls faster than RFRM fission barrier

6. Target P Fus(J) n a p CN E* ER Saddle xn (J) Scission Fission FF FF J() Compound nucleus formation and decay

7. Statistical Model for the decay of compound nucleus • All possibilities for decay are equally likely • Governed r and T. • Important input • Bf • af/an E* Def.

8. Discrepancy in fold distribution 48Ca + 142Nd 190Hg 80Se + 110Pd • Enhancement of the high-spin population for the more symmetric system, brought in by the coupling to inelastic channels. • No enhancement was observed. B. Djerroud et al., PRC 61, 024607 (2000)

9. Fold distribution cont…

10. What happens to ER-fission cross-section ER-fission data not available Available for 40Ar + 148Sm  188Hg (similar to 48Ca + 142Nd) ER data for 86Kr + 104Ru  190Hg (similar to 80Se + 110Pd) Reisdorf et al., NPA444 (1985) 154 Reisdorf et al., NPA438 (1985) 212

12. Entry Spin distribution

13. Summary & Conclusion • Sensitivity of the fission and the ER excitation function • Use of Thomas-Fermi fission barriers produces good agreement • RFRM fission barrier has to be reduced by a factor 0.85 • Inclusion of –3 MeV shell correction in Thomas-Fermi fission barriers produces large discrepancy • ER-fission data and fold distribution data are not consistent • The accuracy of fission barrier height can be checked by comparing the measured fission and ER cross-sections with the statistical model predictions. • Effort should be put to parameterize Thomas-Fermi barrier