1. Fission potential energy surfaces in ten-dimensional deformation space. Vitaly Pashkevich Joint Institute for Nuclear Research. Dubna, Russia Yuri Pyatkov Moscow Engineering Physics Institute. Moscow, Russia Anna Unzhakova St. Petersburg State University. St. Petersburg, Russia

2. 24-28 Sep, 2008 Kazimierz Dolny, Poland 15th Nuclear Physics Workshop "Marie and Pierre Curie“ 70 Years of Nuclear Fission 2 Introduction Fission Potential Energy Surfaces (PES) Strutinsky shell correction model developed in Dubna was designed to make high dimensional calculations possible. Accurate Shape Families in Ten-Dimensional Deformation Spaces Theoretical description of multimodality, exotic and rare fission processes requires more then five nuclear shape degrees of freedom. No Projection to the Three-Dimensional PES has been applied In non-restricted deformation space the influence of magic shell- bounded structures leads to the potential energy minima related to the different fission valleys.

3. 24-28 Sep, 2008 Kazimierz Dolny, Poland 15th Nuclear Physics Workshop "Marie and Pierre Curie“ 70 Years of Nuclear Fission 3 Shape Parameterization Potential energy surfaces are calculated as a liquid drop component with the shell correction by using the single-particle potential of Woods-Saxon type. Nuclear shape is parameterized in the coordinate system associated with Cassini ovaloids with parameters ( ,  n ). Cassini ovaloids – the one-parameter set of curves effective for approximation of nuclear shapes in fission process. The value of basic parameter  = 0 corresponds to sphere,  = 1.1 and 1.2 corresponds to the separated fission fragments after the scission point. R(x) = R 0 (1 +  n  n P n (x))

4. 24-28 Sep, 2008 Kazimierz Dolny, Poland 15th Nuclear Physics Workshop "Marie and Pierre Curie“ 70 Years of Nuclear Fission 4 Discussion P. Möller, D.G. Madland, A.J. Sierk, A. Iwamoto, Nature 409 785 (2001)

5. 24-28 Sep, 2008 Kazimierz Dolny, Poland 15th Nuclear Physics Workshop "Marie and Pierre Curie“ 70 Years of Nuclear Fission 5 Fission barriers vs. elongation and asymmetry PES calculation: symmetrical and two asymmetrical fission valleys

6. 24-28 Sep, 2008 Kazimierz Dolny, Poland 15th Nuclear Physics Workshop "Marie and Pierre Curie“ 70 Years of Nuclear Fission 6 Calculated Binary Fission Valleys ( 252 Cf) Fission valleys 1 – 5 are connected with different dicluster configurations. 1.Cluster radioactivity. 2.Cold binary fission, for which no neck has yet developed. 3. and 4. Two different asymmetrical valleys (B, A). 5. Symmetrical valley. (Qadrupole moment)

7. 24-28 Sep, 2008 Kazimierz Dolny, Poland 15th Nuclear Physics Workshop "Marie and Pierre Curie“ 70 Years of Nuclear Fission 7 Manifestation of Clustering The contour map of the conditional distribution P(M | E * ). The panels depict the shapes of the fissioning system following from the PES calculations ascribed to the two dominant structures.

8. 24-28 Sep, 2008 Kazimierz Dolny, Poland 15th Nuclear Physics Workshop "Marie and Pierre Curie“ 70 Years of Nuclear Fission 8 252 Cf Potential Energy Surfaces Calculation results in deformation space with ten parameters. Cross-sections of the PES for different values of asymmetry.  = (A H - A L )/(A H + A L ) Cross-sections of the PES for different values of asymmetry.  = (A H - A L )/(A H + A L ) Different curves correspond to the bottoms of the potential valleys as a function of quadrupole moment Q.

9. 24-28 Sep, 2008 Kazimierz Dolny, Poland 15th Nuclear Physics Workshop "Marie and Pierre Curie“ 70 Years of Nuclear Fission 9 Cluster Radioactivity Valley Potential energy of the ground state and of the possible configurations at early stages of elongation was calculated in the same ten-dimensional deformation space. Two valleys starting near the ground state differ in the main magic cluster formed inside.

10. 24-28 Sep, 2008 Kazimierz Dolny, Poland 15th Nuclear Physics Workshop "Marie and Pierre Curie“ 70 Years of Nuclear Fission 10 Calculated Binary Fission Valleys ( 246 Cm) The calculation gives us the bottom points of possible fission paths with the parameters of their fine shapes and the corresponding deformation energies. The results for different shape families have been obtained without any changes in the model or its parameters.

11. 24-28 Sep, 2008 Kazimierz Dolny, Poland 15th Nuclear Physics Workshop "Marie and Pierre Curie“ 70 Years of Nuclear Fission 11 Symmetric Compact Configuration Andrzej Staszczak 1,4), Andrzej Baran 1,4), Jacek Dobaczewski 2), Witold Nazarewicz 2,3,4) 1) Institute of Physics, Maria Curie-Sklodowska University, Lublin, Poland 2) Institute of Theoretical Physics, Warsaw University, Warsaw, Poland 3) Department of Physics, University of Tennessee, Knoxville, USA 4) Physics Division, Oak Ridge National Laboratory, Oak Ridge, USA 4 th Int. Conf. on Fission and Properties of Neutron-Rich Nuclei, Sanibel Island, 2007

12. 24-28 Sep, 2008 Kazimierz Dolny, Poland 15th Nuclear Physics Workshop "Marie and Pierre Curie“ 70 Years of Nuclear Fission 12 Conclusions By accurate fission shape families the transition from the one-center to two- or multi-center shell structures is described by Strutinsky Shell Correction Method. Each magic shell-bound configuration produces and develops an individual sheet of the potential energy surface. There is no adiabatic path connecting two different sheets of PES.

13. 24-28 Sep, 2008 Kazimierz Dolny, Poland 15th Nuclear Physics Workshop "Marie and Pierre Curie“ 70 Years of Nuclear Fission 13 Dubna Strutinsky Shell Correction Model V.M. Strutinsky: Shell effects in nuclear masses and deformation energies. 1967 Nucl. Phys. A 95, p. 420 ‘Shells’ in deformed nuclei. 1968 Nucl. Phys. A 122, p. 1 V.V. Pashkevich: On the asymmetric deformation of fissioning nuclei. 1971 Nucl. Phys. A 169, p. 275 Precision shapes of symmetrically fissioning very heavy nuclei. 1988 Nucl. Phys. A 447, p. 1

14. 24-28 Sep, 2008 Kazimierz Dolny, Poland 15th Nuclear Physics Workshop "Marie and Pierre Curie“ 70 Years of Nuclear Fission 14 Overview R.V. Jolos, Yu.V. Palchikov, V.V. Pashkevich, A.V. Unzhakova, Reflection asymmetric deformation and clustering in heavy nuclei Nuovo Cimento, 110 A, 1997 V.V. Pashkevich, A.V. Unzhakova, The Fission barriers of the neutron-deficient actinides Conf. on nuclear spectroscopy and nuclear structure, Obninsk, 1997 V.V. Pashkevich, Yu.V. Pyatkov, A.V. Unzhakova, et al.: 1. Manifestation of clustering in the 252 Cf(sf) and 249 Cf(n th,f) reactions Nuclear Physics A624, 1997 2. Dicluster nuclear configurations in low-energy fission of actinides Conf. Nuclear Structure and Related Topics, Dubna, 1997 3. Magic numbers from 2 to 82 in low-energy fission of actinides Conf. Nuclear Shells – 50 years, St. Petersburg, 1999

15. 24-28 Sep, 2008 Kazimierz Dolny, Poland 15th Nuclear Physics Workshop "Marie and Pierre Curie“ 70 Years of Nuclear Fission 15 Overview 4. Collinear cluster tripartition of actinides: mass-energy correlations of fragments Conf. Clustering phenomena in nuclear physics, St. Petersburg, 2000 5. New indications of collinear tripartition in 252 Cf(sf) studied at the modified FOBOS setup Physics of Atomic Nuclei 66, 2003 6. Cluster-molecular scenario of fission of heavy nuclei at low and middle excitations Conf. Nuclear Structure and Related Topics, Dubna, 2003 7. Nontrivial manifestation of clustering in fission of heavy nuclei at low and middle excitations Physics of Atomic Nuclei 67, 2004 8. Structure of Fission Potential-Energy Surfaces in Ten-Dimensional Deformation Spaces 4 th Int. Conf. on Fission and Properties of Neutron-Rich Nuclei, Sanibel Island, 2007

16. Thank you for your attention!