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Below-barrier paths: multimodal fission & doughnut nuclei A. Staszczak (UMCS, Lublin)

Below-barrier paths: multimodal fission & doughnut nuclei A. Staszczak (UMCS, Lublin). FIDIPRO-UNEDF collaboration meeting on nuclear energy-density-functional methods , Jyväskylä, 9-11 Oct. 2008. M odel. The self-consistent HF+BCS equations are solved using

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Below-barrier paths: multimodal fission & doughnut nuclei A. Staszczak (UMCS, Lublin)

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  1. Below-barrier paths: multimodal fission & doughnut nuclei A. Staszczak (UMCS, Lublin) FIDIPRO-UNEDF collaboration meeting on nuclear energy-density-functional methods,Jyväskylä, 9-11 Oct. 2008

  2. Model The self-consistent HF+BCS equations are solved using the codeHFODD v.2.35that uses the basis expansionmethod in a 3D Cartesian-deformed HO basis. http://www.fuw.edu.pl/~dobaczew/hfodd/hfodd.html The s.p. basis consists of the lowest 1140/1771 stretched HO states originating from the 31 major oscillator shells. The Skyrme functional SkM*is used in the particle-hole channel and a seniority pairingforce is taken in the particle-particle channel.

  3. The self-consistent symmetries: • parity • signature • simplex • time-reversal The symmetry reflection planes mass symmetric fission mass asymmetric fission

  4. Multimodal fission LORW*) group *) LORW group: A. Baran, A. S. (Lublin) W. Nazarewicz (Oak Ridge) J. Dobaczewski(Warszawa)

  5. asymmetricfission (aEF) bimodalfission (sCF & sEF) compact-symmetricfission (sCF)

  6. Z 106 104 102 100 98 N 154 158 156 160

  7. Doughnut nuclei C. Y. Wong, A. S.

  8. Liquid drop model (LDM) with Strutinsky shell corrections J.A. Wheeler (unpublished). C.Y. Wong, Phys. Lett. 41B, 446 (1972). C.Y. Wong, Ann. of Phys. (NY) 77, 279 (1973). C.Y. Wong, Proc. Inter. Symp., Lubbock, 1978, (Pergamon Press, 1979), p. 524. Semiclassical extended Thomas-Fermi (ETF) model with the Skyrme SkM* force X. Viñas, M. Centelles, M. Warda, Int. J. Mod. Phys. E17,177 (2008). Boltzmann-Nordheim-Vlasov (BNV), Boltzmann-Uehling-Uhlenbeck (BUU) kinetic transport models and Monte Carlo simulations … A. Sochocka, R. Płaneta, N.G. Nicolis, Acta Phys. Pol. B 39, 405 (2008). A. Sochocka et al., Int. J. Mod. Phys. E17,190 (2008). Hartree-Fock-Bogoliubov (HFB) theory with the Gogny D1S force M. Warda, Int. J. Mod. Phys. E16, 452 (2007).

  9. d Potential energy curves for toroidal nuclei

  10. 50 MeV

  11. 25 MeV

  12. 12 MeV

  13. KONIEC

  14. The constrained HF procedure: • The constraints act as the external fields capable to deform the nucleus in different ways • The collective coordinates can be defined in a natural way by measuring • the deformations generated by the various constraints The constrained mean field theory defines the deformed states (BCS- or HFB-type) that solve the variational equation: quadratic multipole constraints with the constraint conditions The multipole constraints prescribe different kinds of deformation characterized by the set of parameters

  15. is the many-body nuclear (non-relativistic) Hamiltonian center-of-mass “projection” term (in the VAP technique), to eliminate spurious mode associated with the broken translational symmetry nuclear effective interaction term (Skyrme, Gogne type forces) To describe the fission process most “important” are the low-multipolarity mass moments, i.e., “nuclear stretching” “reflection-asymmetry” “necking”

  16. Seniority pairing: J. Dudek, et al., J. Phys. G6(1980)447. In pairing (BCS) window N (or Z) s.p. states are taken, fn/pparameters are chosen to reproduce pairing gaps ∆n/p for 252Fm. fn= 1.28,fp= 1.11(for SkM*Skyrme force) J. Bartel, et al., Nucl. Phys. A386(1982)79.

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