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ROLE OF THE NON-AXIAL OCTUPOLE DEFORMATION I N THE POTENTIAL ENERGY

ROLE OF THE NON-AXIAL OCTUPOLE DEFORMATION I N THE POTENTIAL ENERGY OF HEAVY AND SUPERHEAVY NUCLEI. XVI NUCLEAR PHYSICS WORKSHOP Kazimierz Dolny 23. – 27.09.2009. PIOTR JACHIMOWICZ, MICHAŁ KOWAL, PIOTR ROZMEJ, JANUSZ SKALSKI, ADAM SOBICZEWSKI. ● Introduction

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ROLE OF THE NON-AXIAL OCTUPOLE DEFORMATION I N THE POTENTIAL ENERGY

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  1. ROLE OF THE NON-AXIAL OCTUPOLE DEFORMATION IN THE POTENTIAL ENERGY OF HEAVY AND SUPERHEAVY NUCLEI XVI NUCLEAR PHYSICS WORKSHOP Kazimierz Dolny 23. – 27.09.2009 PIOTR JACHIMOWICZ, MICHAŁ KOWAL, PIOTR ROZMEJ, JANUSZ SKALSKI, ADAM SOBICZEWSKI

  2. ● Introduction ● Method of calculations ● More about motivation ●Results and discussion ○ Ground–state energy ○ Potential–energy surfaces ● Conclusions Plan of the presentation :

  3. Motivation : ● The importance of nonaxial octupole (tetrahedral) deformation in atomic nuclei was suggested some time ago (J. Dudek et al.). ● One searches for local (global) minima with large (or sizable) a32 on total energy surfaces. a32(Y32 + Y3-2)

  4. Macroscopic-microscopic approach: Method of the calculation : E= Etot(βλµ) – EMACRO (βλµ=0) EMACRO(βλµ)+ EMICRO(βλµ) ○EMACRO(βλµ) = Yukawa + exp ○ EMICRO(βλµ) = Woods – Saxon + pairing BCS

  5. ○We studiedenergy vs. a32 (a one-dimensional calculation) Our try from one year ago : (a32) ○Edef = E(0) – E(a32) ○ values of deformation a32

  6. ○We studiedenergy vs. a32 (a one-dimensional calculation) Our try from one year ago : ○values of deformation a32 (a32) ○ Edef = E(0) – E(a32)

  7. MICRO MACRO ○Edef= E MICRO(0) – E MICRO(a32) ○Edef= E MACRO(0) – E MACRO(a32) MICRO MACRO (a32) Edef= Edef + Edef

  8. Now we include many deformations trying to answer the following: ● Does a tetrahedral (a32) effect survive competition with other deformations in heavy and superheavy nuclei ? ● How large is the effect of a32 on the potential – energy surfaces on top of the axial deformations β2 … β8?

  9. Results : (β2…β8) ○Edef = E(0) – EGS(βλ) (a32) ○ Edef = E(0) – Emin(a32) Edef is much larger than Edef ○ One can suspect that the deformations {βλ}, will strongly decrase or even eliminate the effect of a32 . (β2…β8) (a32)

  10. Results : (a32) ○Edef = E(0) – Emin(a32) (β2…β8) ○ Edef = E(0) – EGS(βλ) Edef is much larger than Edef ○ One can suspect that the deformations {βλ}, will strongly decrase or even eliminate the effect of a32 . (β2…β8) (a32)

  11. Results : (a32,β2…β8) ○Edef = E(0) – EGS(a32 ,βλ) ○ values of deformation a32 ○The GS energies obtained from the minimization in the 8-dimensional deformation space {a32,β2, … , β8}

  12. Results : ○values of deformation a32 (a32,β2…β8) ○ Edef = E(0) – E(a32 , βλ) ○The GS energies obtained from the minimization in the 8-dimensional deformation space {a32,β2, … , β8}

  13. Results : ○The map from the 6-dimensional minimization over {β3, … , β8} at each point

  14. Results : ○The map from the 6-dimensional minimization over {β3, … , β8} at each point

  15. Preliminary results in the region Z ≥110, N ≥146 : ○ first the one-dimensional calculation: (a32) ○Edef = E(0) – E(a32) ○ values of deformation a32

  16. Preliminary results in the region Z ≥110, N ≥146 : ○ first the one-dimensional calculation: ○values of deformation a32 (a32) ○ Edef = E(0) – E(a32)

  17. Energy decomposition into micro and macro parts: MICRO MACRO ○Edef= E MICRO(0) – E MICRO(a32) ○Edef= E MACRO(0) – E MACRO(a32) MICRO MACRO (a32) Edef= Edef + Edef

  18. Comparison between effects of (β2… β8) and a32alone (β2…β8) ○Edef = E(0) – EGS(βλ) (a32) ○ Edef = E(0) – Emin(a32) Edef is larger than Edef (β2…β8) (a32)

  19. Comparison between effects of (β2… β8) and a32alone (a32) ○Edef = E(0) – Emin(a32) (β2…β8) ○ Edef = E(0) – EGS(βλ) Edef is larger than Edef (β2…β8) (a32)

  20. ○The map from the 6-dimensional minimization over {β3, … , β8} at each point

  21. Conclusions : ● Deformation a32 significantly lowers energy of some heavy nuclei with respect to the energy at the spherical shape. ● Since these nuclei are strongly deformed with Edef≈8 MeV, the a32 efect manifests itself mostly as a local minimum in the energy surface, appearing high above the global minimum. ● Around 228Fm we can find global minima with a32, but those minima are very shallow. ● In the superheavyregion wedidn't find any global a32minimum, BUT: one has to note that a32 was the only nonaxial deformation included.

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