1. 9/28/2006 19:01 (00) PAIRING PROPERTIES OF SUPERHEAVY NUCLEI A. Staszczak, J. Dobaczewski and W. Nazarewicz (KFT UMCS) (IFT UW) (ORNL & UT)

2. 9/28/2006 19:01 (00) 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: with the constraint conditions quadratic multipole constraints The multipole constraints prescribe different kinds of deformation characterized by the set of parameters

3. 9/28/2006 19:01 (00) 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”

4. 9/28/2006 19:01 (00) Size of the basis 1140 s. p. states of deformed 3D h. o.

5. 9/28/2006 19:01 (00) Seniority pairing: J. Dudek, et al., J. Phys. G6 (1980)447. Zero-range pairing force: R. R. Chasman, Phys. Rev. C 14 (1976)1935. G. F. Bertsch and H. Esbensen, Ann. Phys. (N.Y.) 209 (1991)327. In the paring (BCS) window  n/p  N (or Z) s. p. states are taken, and parameters are chosen to reproduce  n/p for 252 Fm.

6. 9/28/2006 19:01 (00) The spectral (average) gap:

7. 9/28/2006 19:01 (00) SLy4

8. 9/28/2006 19:01 (00) SLy4

9. 9/28/2006 19:01 (00) SLy4

10. 9/28/2006 19:01 (00) SLy4

11. 9/28/2006 19:01 (00) Quadrupole Moment Q 20 [b] Total Energy E tot [MeV] Hexadecapole Moment Q 40 [b 2 ]    E tot    Q 40    E tot    Q 40 MIX SLy4

12. 9/28/2006 19:01 (00)    E tot   n   p    E tot   n   p Quadrupole Moment Q 20 [b] Total Energy E tot [MeV] Pairing Gap  n/p [MeV] MIX SLy4

13. 9/28/2006 19:01 (00)Summary We compared “volume”, “surface” and “mixed” zero-range nuclear pairing forces with monopole pairing. Applying “mixed”  -interaction we have investigated total binding energies (barriers) and spectral pairing gaps along fission paths of even-even superheavy nuclei with N = 184.

14. 9/28/2006 19:01 (00) KONIEC

15. 9/28/2006 19:01 (00) P. Möller, J. R. Nix, and K.-L. Kratz Atomic Data’97

16. 9/28/2006 19:01 (00) Quadrupole Moment Q 20 [b] Total Energy E tot [MeV] Hexadecapole Moment Q 40 [b 2 ] G SLy4

17. 9/28/2006 19:01 (00) Quadrupole Moment Q 20 [b] Total Energy E tot [MeV] Pairing Gap [MeV]    E tot   n   p    E tot   n   p G SLy4

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