Description of experimental fission barriers of heavy nuclei I.Introduction II.Experimental barriers III.Method of description IV.Deformation space V.Results and discussion VI.Conclusions 15th Nuclear Physics Workshop: 70 Years of Nuclear Fission Sept , 2008, Kazimierz Dolny, Poland M. Kowal, L. Shvedov and A. Sobiczewski Sołtan Institute for Nuclear Studies, Warsaw, Poland

I. Introduction 1.Region of our interest: SHN (Z= ) 2. Motivation: cross sections  (~1 pb  ~50 fb)  B f st 3. Present state of HN : (map of SHN) 3.Role of B f st - sensitivity of  to B f st - a need for a large accuracy of B f st 4.Two configurations important for B f st - eq. and s.p. (example of fission barrier) 5.Concentration on even-even nuclei

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

II. Experimental barriers 1. Bexp for only nuclei closest to SHN are used (Z=92-98) 2. They are derived from exp in not a very direct way (a model is used) 3. Estimated uncertainty: about MeV (?)

III. Method Macro-micro (same as used for description of many properties of HN) Etot = Emacr + Emicr Emacr = Yukawa + exp Emicr = shell corr. IV. Deformation space 1. As large as possible 2. Larger space, better description of the properties (e.g. mass, especially B f st and T sf ) 3. Specification of the space: axial, non-axial and reflection-asymmetric shapes included

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

V. Results 1. Comparison between Bth and Bexp for few variants of calculations in the Z=92-98 region 2. Comparison between Bth for few variants of calculations in a large region of nuclei

VI. Conclusions 1.It is hard to say how accurately Bexp are determined ( MeV?) in the U-Cf region. 2.The average inaccuracy of theoretical description of Bexp is rather large (about MeV). 3.Discrepancy between various theor. descriptions in the SHN is very large( up to more than 5 MeV !). –Not comfortable situation for people calculating σ. –More study is needed.

Conclusions 1. Shapes and shell correction of HN have been studied at two configurations: equil. (ground state) and saddle point. 2. For an accurate study, a large deformation space is needed (10-dimensional space has been used). 3. Equil. config.: - the shapes are axially- and reflection-symmetric for all studied nuclei - shell correction is large (up to about 9 MeV for a doubly magic def. nucleus with Z=108, N=162 and a spherical one with Z=114, N=184). 4. Sadlle-point config.: - shapes are generally non-axial, but reflection sym.; only lighter nuclei (around uranium and below) are reflection asym. at their saddle point. - shell corr., although smaller than at equil., is still large (up to about 2.5 MeV). It should not be disregarded (as quite often done). - effect of non-axiality is large, up to more than 2 MeV. This is a big effect, if one keeps in mind that a 1 MeV change in B f st changes the calculated σ by one order of magnitude or even more.

Coworkers: Michał Kowal and Leonid Shvedov