1. Fission barriers of heavy and superheavy nuclei analyzed in multidimensional deformation space I.Introduction II.Method III.Deformation space IV.Results and discussion V.Conclusions XIII Nuclear Physics Workshop Kazimierz Dolny, 27. 09 - 1.10. 2006 M. Kowal, L. Shvedov and A. Sobiczewski Sołtan Institute for Nuclear Studies, Warsaw, Poland

2. I. Introduction 1.Two main problems with heaviest nuclei (HN): cross sections  (~1 pb  ~50 fb)  B f st half-lives 2.Present state of HN (f1,f1a) 3.Role of B f st (f2) sensitivity of  to B f st a need for a large accuracy of B f st

3. 98 99 100 101 102 103 104

5. II. Method Macro-micro (same as used for description of many properties of HN) III. Deformation space 1. As large as possible 2. Larger space, better description of the properties (e.g. mass, especially T sf ) 3. Specification of the space: axial, non-axial and reflection-asymmetric shapes included

7. A large, 10-dimensional space One to one correspondence between values of parameters and shape

8. IV. Results 1. Axial symmetry - example: 278 112(f4) - dependence on max (f5) 2. Quadrupole non-axiality ( =2) (f6-8) - mechanism of decreasing B f st by non-axial shapes 3. Hexadecapole non-axiality ( =4) (f9-9a) - also a discussion by M. Kowal 4. Comparison with exp. (f10) 5. Reflexion asymmetry (f11)

9. The barrier: thin but high, created totally by shell effects

15. Effect of total hexadecapole deformation

16. Effect of non-axial hexadecapole deformations

17. Effect of non-axiality parameter

19. Effect of reflection-asymmetric deformations

20. Conclusions 1.Barriers of HN are totally created by shell effects. They are thin, but high. 2.Their height B f st strongly depends on the deformation space, in which they are calculated. 3.An increase of the dimension of the space results in an increase of B f st for deformed nuclei, and in a decrease of it for spherical ones, in the case of axial symmetry. 4.Non-axial shapes are important for B f st. They may decrease it by up to about 2 MeV. This is again due to shell effects, because macr. part of the energy is stiff against non-axiality. Only after the inclusion of non-axiality, calculated B f st well reproduces exp. value of it. 5.Reflexion-asymmetric shapes do not contribute to B f st for heaviest nuclei.

21. B F =4 MeV