Pre-scission shapes of fissioning nuclei
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1 Pre-scission shapes of fissioning nuclei Micha l Warda Uniwersytet Marii Curie-Sk lodowskiej Lublin, Poland SSNET Workshop Gif-sur-Yvette,
2 Collaboration: J.L. Egido, UAM, Madrid W. Nazarewicz, MSU, East Lansing K. Pomorski, UMCS, Lublin L.M. Robledo, UAM, Madrid A. Staszczak, UMCS, Lublin A. Zdeb, UMCS, Lublin
3 Outline: Theoretical framework Symmetric and asymmetric fission Neutron-deficient Hg region: 18 Hg, 198 Hg, 196 Po, 174 Pt Cluster radioactivity in actinides Super-heavies Conclusions
4 Calculations of potential energy surfaces Self-consistent calculations in Hartree-Focka-Bogolubov theory Gogny D1S parameter set Potential energy surfaces calculated with constrains on quadrupole, octupole and hexadecapole moments Pre-scisssion configuration determines properties of fission fragments
5 - bimodal fission Hulet et al., PRL56, 313 (1986). Hulet et al., PRC4, 77 (1989).
6 Q 2 = 15 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
7 Q 2 = 25 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
8 Q 2 = 35 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
9 Q 2 = 45 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
10 Q 2 = 55 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
11 Q 2 = 65 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
12 Q 2 = 75 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
13 Q 2 = 85 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
14 Q 2 = 95 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
15 Q 2 = 15 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
16 Q 2 = 115 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
17 Q 2 = 125 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
18 Q 2 = 135 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
19 Q 2 = 145 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
20 Q 2 = 155 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
21 Q 2 = 165 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
22 Q 2 = 175 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
23 M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
24 Q 2 = 9 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
25 Q 2 = 11 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
26 Q 2 = 13 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
27 Q 2 = 15 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
28 Q 2 = 17 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
29 Q 2 = 19 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
30 Q 2 = 21 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
31 Q 2 = 23 b M. Warda, J.L Egido, L.M. Egido, K. Pomorski, Phys. Rev. C 66 (22) 1431
32
33 pre-scission point 2 Q N D ρρ Q 3 = b 3/2 Q 3 =66.7 b 3/ Neck parameter: Q N = exp ( (z z ) 2 ) a Density distance: D ρρ, = ρ( r) ρ ( r) dτ N. Dubray, D. Regnier, CPC183, 235 (212). M. Warda, A. Zdeb, Phys. Scr. 9, 1143 (215).
34 1 (a) 2 (b) 5 15 r [fm] σ(z) Cd 124 Cd z [fm] z [fm].2 (c).2 (d) ρ [fm -3 ].1 ρ [fm -3 ] Cd 124 Cd. 124 Cd 124 Cd z [fm] z = -7.1 fm z = 7.1 fm r [fm]
35 1 5 (a) 2 15 (b) r [fm] σ(z) Sn 16 Mo z [fm] z [fm].2 (c).2 (d) ρ [fm -3 ].1 ρ [fm -3 ].1 16 Mo 132 Sn 132 Sn 16 Mo z = -9 fm z = 11.5 fm z [fm] r [fm]
36 18 Hg FIG. 4 (color online). The derived fission-fragment distribution of 18 Hg as a function of the fragment mass and the total kinetic energy. FIG. 5 (color online). A schematic representation of the potential-energy surface for 18 Hg in two dimensions (elongation and asymmetry) resulting from a five-dimensional analysis. The shapes shown, connected by arrows to their locations, are the ground state, the saddle point, and the point where the asymmetric valley disappears. A.N. Andreyev, et al., Phys. Rev. Lett. 15 (21) J. Elseviers, et al., Phys. Rev. C 88 (213) 44321
37 18 Hg Hg M. Warda, A. Staszczak, W. Nazarewicz, Phys. Rev. C 86 (212) 2461
38 r (fm) Zr 18 Hg 72 Ge z (fm) M. Warda, A. Staszczak, W. Nazarewicz, Phys. Rev. C 86 (212) 2461
39 σ(z) σ 1 max z half 1,out σ min σ(z) = 2π dr r ρ(z, r ) z half 1,in z [fm] σ 2 max M. Warda and A. Zdeb, Phys. Scr. 9 (215) 1143
40 198 Hg Hg M. Warda, A. Staszczak, W. Nazarewicz, Phys. Rev. C 86 (212) 2461 M.G. Itkis, et al., Yad. Fiz. 52, 944 (199)
41 Po P P1 P8 P2 P6 P4 P5 P3 P7 P9 4 fussion path
42 196 Po L. Ghys, et al. Phys. Rev. C 9 (214) 4131R
43 P6 P5 P P
44 P3 Q 3 = P7 P9 Q 2 = 25 b
45 Cluster radioactivity 223 Ra C+29 Pb Rose and Jones, Nature 37, 245 (1984) R. Bonetti, A. Guglielmetti, in Heavy Elements and Related New Phenomena Vol II, ed. W. Greiner and R.K. Gupta, p.634, Word Scientific, 1999 M. Warda Pre-scission shapes of fissioning nuclei
46 Cluster radioactivity: 238 Pu 238 Pu Q2 =14.1 b Q 3 = b 3/2 238 Pu z [fm] Q 2 = -28 b r p [fm] M. Warda, L.M. Robledo, Phys. Rev. C 84 (211) 4468
47 Cluster radioactivity: 238 Pu 238 Pu Q2 =17.3 b Q 3 =1 b 3/2 238 Pu z [fm] Q 2 = -28 b r p [fm] M. Warda, L.M. Robledo, Phys. Rev. C 84 (211) 4468
48 Cluster radioactivity: 238 Pu 238 Pu Q2 =25.4 b Q 3 =2 b 3/2 238 Pu z [fm] Q 2 = -28 b r p [fm] M. Warda, L.M. Robledo, Phys. Rev. C 84 (211) 4468
49 Cluster radioactivity: 238 Pu 238 Pu Q2 =33.3 b Q 3 =3 b 3/2 238 Pu z [fm] Q 2 = -28 b r p [fm] M. Warda, L.M. Robledo, Phys. Rev. C 84 (211) 4468
50 Cluster radioactivity: 238 Pu 238 Pu Q2 =4.2 b Q 3 =4 b 3/2 238 Pu z [fm] Q 2 = -28 b r p [fm] M. Warda, L.M. Robledo, Phys. Rev. C 84 (211) 4468
51 Cluster radioactivity: 238 Pu 238 Pu Q2 =47.3 b Q 3 =5 b 3/2 238 Pu z [fm] Q 2 = -28 b r p [fm] M. Warda, L.M. Robledo, Phys. Rev. C 84 (211) 4468
52 Cluster radioactivity: 238 Pu 238 Pu Q2 =43.2 b Q 3 =6 b 3/2 238 Pu z [fm] Q 2 = -28 b r p [fm] M. Warda, L.M. Robledo, Phys. Rev. C 84 (211) 4468
53 Cluster radioactivity: 238 Pu 238 Pu Q2 =62.1 b Q 3 =7 b 3/2 238 Pu z [fm] Q 2 = -28 b r p [fm] M. Warda, L.M. Robledo, Phys. Rev. C 84 (211) 4468
54 Cluster radioactivity: 238 Pu 238 Pu Q2 =68. b Q 3 =8 b 3/2 238 Pu z [fm] Q 2 = -28 b r p [fm] M. Warda, L.M. Robledo, Phys. Rev. C 84 (211) 4468
55 Super-heavy nuclei Hs Cn M. Warda, J.L. Egido, Phys. Rev. C 86 (212) 14322
56 266 Hs refl. symm. fission path octupole fission path -5 refl. symm. fusion path -6 octupole fusion path
57 Fission half-lives fission RS fission NRS protons neutrons -5-1 A. Baran, M. Kowal, P.G. Reinhard, L.M. Robledo, A. Staszczak, M. Warda, Nucl. Phys. A 944 (215) 442
58 Conclusions Pre-scission shapes have been determined in self-consistent procedure in HFB theory with Gogny D1S force The fragment mass asymmetry reproduces experimental observations Shell structure of the fragments can be seen before the neck rupture
59 3rd Symposium on Superheavy Elements Kazimierz Dolny, Poland 1-14 September 217 UMCS Lublin, NCNR Warsaw, University of Warsaw, JINR Dubna XXIV Nuclear Physics Workshop Kazimierz Dolny, Poland 2-24 September 217 Spontanous Symmetry Breaking in Nuclear Physics 2th anniversary of the first paper of Stefan Frauendorf and Jie Meng on chirality UMCS Lublin, HIL University of Warsaw
60
61 18 Hg.2 (d) 18 Hg saddle point (a) Hg, saddle point, N/Z = 1.25, Q2 = 26 b, Q 3 = 33.8 b 3/2 Q N (z =.5 fm) =.3 A=11 A=79 ρ [fm -3 ].15.1 r perp = r perp [fm] -5 Q 2 = b z = 1.2 fm Q 2 = 8 b.5 9 Zr ground state 72 Ge deformed 9 Zr, ground state, N/Z = Ge, deformed, N/Z = z [fm] (b) (c) Zr Ge Q 2 = 2.6 b E =.7 MeV ρ [fm -3 ] z [fm].2 18 Hg, saddle point, z = -8 fm 18 Hg, saddle point, z = 1 fm 9 Zr 72 Ge, deformed.15 ground state Q 2 = 8 b E = 3.4 MeV Q 2 = -2.7 b Hg saddle point (e) neck, z = 1 fm r perp [fm]
62 198 Hg.2 (d) 198 Hg saddle point (a) Hg, saddle point, N/Z = 1.475, Q2 = 33 b, Q 3 = 11.5 b 3/2 Q N (z = 1.5 fm) =.3 A=18 A=9 ρ [fm -3 ].15.1 r perp = r perp [fm] -5 Q 2 = 12 b 98 Zr, deformed, N/Z = 1.45 z = 1.47 fm Q 2 = 2.4 b 8 Ge, ground state, N/Z = z [fm] (b) (c) Zr Ge.5 98 Zr deformed 8 Ge ground state z [fm] Hg, saddle point, z = -8.5 fm 198 Hg, saddle point, z = 1.5 fm 98 Zr, deformed 8 Ge ground state, Q 2 = 7.8 b E =.6 MeV ρ [fm -3 ].1 Q = -4.3 b Q 2 = 12 b E = 1.1 MeV Q 2 = 2.4 b Hg saddle point (e) neck, z = 1.5 fm r perp [fm]
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