1. SUPERDEFORMED OBLATE SUPERHEAVY NUCLEI ? SDO minima Stability of SDO nuclei K-isomerism Discussion Summary P. Jachimowicz, M. Kowal, J. Skalski

2. Macroscopic-microscopic approach: Macroscopic-microscopic approach: E = E tot ( β λ µ ) – E MACRO ( β λ µ = 0) E = E tot ( β λ µ ) – E MACRO ( β λ µ = 0) E MACRO ( β λ µ )+ E MICRO ( β λ µ ) ○ E MACRO ( β λ µ ) = Yukawa + exp ○ E MICRO (β λ µ ) = Woods – Saxon + pairing BCS ○ E MICRO (β λ µ ) = Woods – Saxon + pairing BCS

3. Shape Parametrization : 12-DIM !

4. Numerical tests and error checks 1.Monitoring of: energy gradients continuity of the resulting deformation parameters stability with respect to the choice of starting values 2. The starting values of deformation parameters were always taken different from zero 3. For several nuclei, we repeated the minimization for the whole map by choosing starting values randomly

5. SDO minima

6. YpE

8. LSD LSD  1 MeV deeper minima!

9. D1S Gogny force  competing SDO minima (thanks Michał Warda)

11. With half-lives T_{1/2}<10^{-5} s - the present limit for detection of synthesized superheavy nuclei - superheavy SDO systems might be considered merely as a theoretical curiosity.

12. Fission

13. Alpha decay Formula a’laViola Seaborg from Royer

14. One proton emission half lives

15. Beta decay Since for high-K isomers |M| is reduced, their beta+ decay is even slower.

16. A fascinating possibility for their longer life-times is related to K-isomerism, high-K configurations at the SDO shape are very likely!!! (13/2-)+(7/2)+=>10-(15/2+)+(9/2)-=>12- OPTIMAL CONFIGURATION:

17. K-isomerism (discussion) ! FISSION HINDRANCE: T_{sf} for odd and odd-odd heavy and superheavy nuclei are by 3-5 orders longer than for their even-even neighbours. Increase was found for high-K isomers, with respect to (prolate) shape isomers on which they are built, in even 240Cm-244Cm. For SDO superheavy K-isomers two factors combine to increase fission half-life: A) the axial fission path is closed by the conservation of the K quantum number. B) triaxial barriers increase due to a decrease in pairing caused by the blocking of two neutrons or protons. C) additional hindrance of fission is expected for configurations involving blocked high-Omega intruder states. ALPHA HINDRANCE: High-K isomer in 270Ds has longer (partial) half-live T_{alpha}= 6.0 ms than the g.s., T_{alpha}(g.s.)=100 microsec. For SDO nuclei, an additional hindrance may result from a difference between the parent and daughter high-K configuration. Extra excitation in the daughter, leading to a smaller Q_{alpha}.

18. Summary Summarizing, our study shows that starting with standard macro-micro method in multidimensional deformation space one obtains super-deformed oblate shapes in the ground- or low excited state for very heavy nuclei. Although relatively small barriers could not protect these SDO states from quick fission, high-K isomerism can increase their stability. The present knowledge on the stability of K-isomers makes likely that at least some of these SDO nuclei could be detected with the present technique, if produced.