Microscopic description of fission in the neutron-deficient Pb region

Microscopic description of fission in the neutron-deficient Pb region Micha l Warda Maria Curie-Sk lodowska University, Lublin, Poland INT Seattle, 1-1-213

Fr 87 At 85 Rn 86 Po 84 Bi 83 Pb 82 Tl 81 Pb 28 Hg 8 Au 79 Pt 78 9 92 94 96 98 1 12 14 16 18 11 112 114 116 118 12 122 124 126 128 13

18 Tl(Z=81,N=99) I=(4,5) Q EC 1.44 MeV 18 Hg(Z=8 N=1) β + /EC N β γ γ γ Low-energy fission! (E*~3-12 MeV, limited by Q EC ) Relatively low angular momentum of the state 12 cases known before our work (neutron-deficient Uranium region) B f ~ 1 MeV βdf N βdf deformation βdf branch P βdf = N βdf N β A.N. Andreyev, FUSTIPEN 212, Semminar

9 8 b) 7 6 5 4 3 2 3 4 5 6 7 8 9 FIG. 2. (a) Singles -decay energy spectrum from both Si detectors; (b) Si-Si coincidence spectrum in the fission-energy region. The two-peaked structure in (b) originates because the two fission fragments have different energies, a direct result of the asymmetric mass distribution. FIG. 4 (color online). The derived fission-fragment distribution of 18 Hg as a function of the fragment mass and the total kinetic energy. A.N. Andreyev, et al. PRL 15, 25252 (21).

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.

M.G. Itkis, et al., Yad. Fiz. 52, 944 (199).

Calculations details Microscopic Hartree-Focka-Bogolubov theory Gogny D1S parameter set Constrains on quadrupole, octupole and hexadecapole moments as well as on the neck parameter Excitations of nuclei were not taken into account

Fission barriers in 18 Hg and 198 Hg 3 3 2 18 Hg 2 E [MeV] 1 E [MeV] 1 198 Hg -1 5 1 15 2 25 3 35 5 1 15 2 25 3 35 M. Warda, A. Staszczak, W. Nazarewicz, PRC 86, 2461 (212).

5 2 5 35 4 18 Hg 15 4 198 Hg 3 25 Q 3 [b 3/2 ] 3 2 P1 1 Q 3 [b 3/2 ] 3 2 P1 2 15 1 P2 5 1 1 5 P2 5 1 15 2 25 3 5 1 15 2 25 3 35 A H /A L = 11/79 A H /A L = 18/9

A. Staszczak M. Warda, Fission in the neutron-deficient Pb region Microscopic description of fission in the neutron-deficient Pb r

r (fm) 5-5 9 Zr 18 Hg 72 Ge -15-1 -5 5 1 15 z (fm) (i) reproduce N/Z ratio (ii) reproduce half of the mass of the outer part (iii) reproduce mass distribution

energy fission barrier E scission scission point Coulomb repulsion Q fission E Coulomb (scission) elongation E scission = E Coul (scission) Q

3 2.8 18 Hg. ρ [fm -3 ].16 1 258 Fm ρ [fm -3 ].16.8 E [MeV] 1 D = 3.4 fm -1 1 z [fm] E [MeV]. D = 3.5 fm -1 1 z [fm].16.16 ρ [fm -3 ].8-1 ρ [fm -3 ].8. D = 4.6 fm -1 1 z [fm] -2. D = 4.5 fm -1 1 z [fm] -1 5 1 15 2 25 3 35 5 1 15 2 25 3 35 Q = 157.3 MeV E Coul (2R + 4 fm) = 167.5 MeV E scission = 1.3 MeV Q = 251.7 MeV E Coul (2R + 4 fm) = 238. MeV E scission = 13.7 MeV

178 Hg 2 Hg 3 178 Hg 18 Hg compact fission scission point 182 Hg E [MeV] 2 1 Q 3 = A C E A C A E C 184 Hg A E C E [MeV] 3 2 1 186 Hg A E D C 188 Hg fussion path E D B 19 Hg E B D F E D B 192 Hg E [MeV] 3 2 1 F B 194 Hg F B 196 Hg F B 198 Hg F B 2 Hg 5 1 15 5 1 15 5 1 15 5 1 15

Fragments mass distribution: 8 9 1 11 8 9 1 11 194 Po 196 Po A. Andreyev, L. Ghys, priv. comm.

E [MeV] 14 12 1 8 6 196 Po P P1 P8 P2 P6 P5 P4 P9 P3 P7 4 fussion path 2-5 5 1 15 2 25 3

3 2 1-1 196 Po -2 5 1 15 2 25 3 12 3 45 Q 3 [b 3/2 ]

5 4 196 Po P4 Q 3 [b 3/2 ] 3 2 P1 P5 1 P2 P7 P3 P6 P9 5 1 15 2 25 3

A H /A L = 13/93 3 196 Po 25 2 Q 3 [b 3/2 ] 15 1 P5 3 5 P3 25 P6 Q 3 [b 3/2 ] 2 15 1 5 22 23 24 25 26 27 28 29 3 3 25 P9 22 23 24 25 26 27 28 29 3 A H /A L = 98/98 Q 3 [b 3/2 ] 2 15 1 5 P5 P7 A H /A L = 99/97 P6 22 23 24 25 26 27 28 29 3

3 25 2 Q 3 [b 3/2 ] 15 1 5 P6 P5 P7-5 -1 P3-15 22 23 24 25 26 27 28 29 3

Q 2 = 25 b

P3 Q 3 = -3.7 b 3/2 Q 3 = P7 Q 3 = 6.1 b 3/2 P9 Q 3 = Q 2 = 25 b

1 P3 Q 4 [b 2 ] 95 9 P7 85 8 P9 196 Po Q2 = 24 b -1-5 5 1 Q 3 [b 3/2 ]

115 11 P3 Q 4 [b 2 ] 15 P7 1 95 P9 196 Po Q2 = 26 b -1-5 5 1 Q 3 [b 3/2 ]

14 5 E [MeV] 12 1 8 6 194 Po P P1 P2 P6 P3 P2 P9 P1 Q 3 [b 3/2 ] 4 3 2 194 Po P1 4 fussion path 2-5 5 1 15 2 25 3 1 P2 P3 P6 P9 5 1 15 2 25 3 P3: A H /A L = 11/93 P9: A H /A L = 97/97

25 25 2 P1 2 Q 3 [b ] 15 1 Q 3 [b 3/2 ] 15 1 5 P2 P3 5 P6 P9 16 18 2 22 24 26 28 16 18 2 22 24 26 28

Conclusions: Potential energy surface of nuclei from neutron deficient Hg region were determined in the microscopic calculations Fragment mass asymmetry of 18 Hg and 198 Hg is reproduced Plateau of the PES at large quadrupole deformations is found around N=11 Unexpected reflection asymmetric shapes with vanishing octupole moment were found