THE FISSION BARRIERS OF SUPERHEAVY AND EXOTIC NUCLEI Fedir A. Ivanyuk 1 and Krzysztof Pomorski 2 1 Institut for Nuclear Research, Kiev, Ukraine 2 Theoretical 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

For E micr see 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 MeV for known nuclei withZ>70

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

Optimal shapes

Deformation energy

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

Modified Funny Hills shape parametrization deviation < 150 keV

Surface curvature energy Leptodermous expansion: ETF = E vol + E surf + E curv + E Gcurv

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

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 E micr see P. Moeller, J. R. Nix, W. D. Myers and W. J. Swiatecki, At. Data and Nucl. Data Tables, 59, 249 (1995).

Barriers of light nuclei 75 Br 35, 90 Mo 42, 94 Mo 42, 98 Mo 42

Mass asymmetry

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

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 MeV, a value that is comparable with the experimental uncertainties.

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Mass-asymmetric shapes

Mass asymmetric shapes, x = 0.75

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