THE FISSION BARRIERS OF SUPERHEAVY AND EXOTIC NUCLEI

1. THE FISSION BARRIERS OF SUPERHEAVYAND EXOTIC NUCLEI Fedir A. Ivanyuk1 and Krzysztof Pomorski2 1Institut for Nuclear Research, Kiev, Ukraine 2Theoretical Physics Division, UMCS, Lublin, Poland The variational principle for liquid drop shapes The account of curvature energy The fission barriers within LSDrop model The semi-analytical expression for the barrier heights based on the topological theorem Numerical results, mass-asymmetric shapes Summary and outlook

2. For Emicrsee P. Moeller, J. R. Nix, W. D. Myers and W. J. Swiatecki, At. Data and Nucl. Data Tables, 59, 249 (1995). The rms-deviation is 1.113 MeV for known nuclei withZ>70

3. V.M.Strutinsky et al, Nucl. Phys. 46, 659 (1963)

4. Optimal shapes

5. Deformation energy

6. R.W.Hasse, W.D.Myers, Geometrical Relationships of Macroscopic Nuclear Physics:

7. Modified Funny Hills shape parametrization deviation < 150 keV

8. Surface curvature energy Leptodermous expansion: ETF = Evol+ Esurf + Ecurv + EGcurv

9. The LSD barrier heights K.Pomorski and J. Dudek, Phys. Rev. C 67, 044316 (2003) F.A.Ivanyuk and K.Pomorski, Phys: Rev. C 79, 054327 (2009) The rms dev.for 35<Z< 105, 0<I< 0.3 is 150 keV

10. The barrier heights, topological theorem W. D.Myers and W. J. Swiatecki, Nucl. Phys. A601, 141 (1996): the “barrier will be determined by a path that avoids positive shell effects and has no use for negative shell effects. Hence the saddle point energy will be close to what it would have been in the absence of shell effects, i.e., close to the value given by the macroscopic theory!” For Emicrsee P. Moeller, J. R. Nix, W. D. Myers and W. J. Swiatecki, At. Data and Nucl. Data Tables, 59, 249 (1995).

11. Barriers of light nuclei 75Br35 , 90Mo42 ,94 Mo42 , 98Mo42

12. Mass asymmetry

13. The temperature dependence of the LSD-barriers B. Nerlo-Pomorska, K. Pomorski and J. Bartel, Phys. Rev. C 74, 034327 (2006)

14. Summary • The optimal shapes of fissioning nuclei are studied within the Lublin-Strasbourg drop model • The liquid drop fission barriers were calculated for isotopic chains in the range 35< Z < 110 and a simple approximation for the liquid drop fission barriers heights containing only Z and (N-Z)/A is obtained. • The topological theorem by Myers and Swiatecki was used to express the fission barrier height as the sum of the macroscopic barrier height and the ground-state shell correction. This provides a very simple method to calculate fission barrier heights. In addition to the ground-state shell • correction, which should be taken from the tables, one only has to calculate simple analytical estimate for the liquid drop part of the barrier height. • The rms deviation of calculated versus experimental values of fission-barrier heights for known nuclei with Z < 70 is 1.113 MeV, a value that is comparable with the experimental uncertainties.

15. Dear colleagues, This is the first circular of the 3-rd International Conference on Current Problems in Nuclear Physics and Atomic Energy (NPAE-Kyiv2010), which will be held from June 7 to June 12, 2010 in Kyiv, Ukraine. The NPAE-Kyiv2010 conference will cover the following topics: Collective processes in atomic nuclei Nuclear reactions Nuclear structure and decay processes Rare nuclear processes Neutron and reactor physics, nuclear data Problems of atomic energy Applied nuclear physics in medicine and industry Experimental facilities and detection techniques

16. Mass-asymmetric shapes

17. Mass asymmetric shapes, x = 0.75

18. K.T.R.Davies and A.J.Sierk, Phys.Rev.C 31 (1985) 915