Role of octupole deformed shell effects on the fission of nuclei - PowerPoint PPT Presentation

April 16-18, 2019 Role of octupole deformed shell effects on the fission of nuclei from actinides to mercury region Guillaume SCAMPS Collaboration : C. Simenel

Motivation : understand the shell effects on fission Empirical behavior of actinide nuclei J.P. Unik, J.E. Gindler, J.E. Glendenin et al. : Proc. Phys. Data from D. A. Brown et al., Endf/b-viii.0, Nucl. Data and Chem. of Fission IAEA Sheets 148, 1 (2018), (spontaneous and thermal Vienna , Vol II, 20 (1974) neutron-capture). Motivation How can we understand this behavior ? Interplay between structure and reaction ?

Mean-field theory with pairing TDHF TDHFB Pairing correlation Independent particle Initialisation : ˆ Quasi-particles : | ω α � = � U α � h MF | φ i � = ǫ i | φ i � V α Evolution : Evolution : i � d | ω α � ∆ i � d ρ = � h � dt = [ h MF , ρ ] | ω α � − ∆ ∗ − h ∗ dt TDHF+BCS Based on TDHFB with the approximation : ∆ ij = δ ij ∆ i dt = (ˆ Evolution : i � d φ i h MF − ǫ i ) φ i i � dn i dt = ∆ ∗ i κ i − ∆ i κ ∗ i i � d κ i dt = κ i ( ǫ i − ǫ i ) + ∆ i (2 n i − 1)

New systematic study First : CHF+BCS Example : 240 Pu -1790 Second : TDHF+BCS Symmetric -1795 Asymmetric -1800 -1805 E [MeV] -1810 -1815 -1820 -1825 -1830 -1835 0 20 40 60 80 100 120 Q 20 [b] Details of the calculation Skyrme functionnal Sly4d Surface pairing interaction ∆ x = 0.8 fm Lattice : L x × L y × 2 L z = 40 × 19.2 × 19.2 fm 3

New systematic study First : CHF+BCS Example : 240 Pu -1790 Second : TDHF+BCS Symmetric -1795 Asymmetric -1800 -1805 E [MeV] -1810 -1815 -1820 -1825 -1830 -1835 0 20 40 60 80 100 120 Q 20 [b] Details of the calculation Skyrme functionnal Sly4d Surface pairing interaction ∆ x = 0.8 fm Lattice : L x × L y × 2 L z = 40 × 19.2 × 19.2 fm 3

New systematic study First : CHF+BCS Example : 240 Pu -1790 Second : TDHF+BCS Symmetric -1795 Asymmetric -1800 -1805 E [MeV] -1810 -1815 -1820 -1825 -1830 -1835 0 20 40 60 80 100 120 Q 20 [b] Details of the calculation Skyrme functionnal Sly4d Surface pairing interaction ∆ x = 0.8 fm Lattice : L x × L y × 2 L z = 40 × 19.2 × 19.2 fm 3

TDHF+BCS systematics results Comparison with experimental data TDHF+BCS 90 230 Th 88 86 N H 234 U 84 82 236 U Yield (arbitrary units) 240 Pu 56 246 Cm Z H 54 52 250 Cf 50 30 35 40 45 50 55 60 230 Th 234 U 236 U 240 Pu 246 Cm 250 Cf Proton number Z A

TDHF+BCS systematics results Comparison with experimental data TDHF+BCS 90 230 Th 88 86 N H 234 U 84 82 236 U Yield (arbitrary units) 240 Pu 56 246 Cm Z H 54 52 250 Cf 50 30 35 40 45 50 55 60 230 Th 234 U 236 U 240 Pu 246 Cm 250 Cf Proton number Z A Conclusion : The TDHF+BCS calculation reproduces well the Z=54 behavior. But why ?

Nucleon localization function Fermion localization function � 2 � − 1 � 4 |∇ ρ q σ | 2 − j 2 � τ q σ ρ q σ − 1 q σ C q σ ( r ) = 1 + ρ q σ τ TF q σ A. D. Becke and K. E. Edgecombe, J. Chem. Phys. 92, 5397 (1990). Physical meaning : C ∈ [0 : 1] C q σ ( r ) = 1 Probability to find another particle with the same q and σ very low. C q σ ( r ) = 0 . 5 Limit of uniform-density Fermi gas. Mask function : → C q σ ( r ) ρ q σ ρ max q σ

Nucleon localization function Example : Fermion localization function � 2 � − 1 � 4 |∇ ρ q σ | 2 − j 2 τ q σ ρ q σ − 1 � q σ C q σ ( r ) = 1 + ρ q σ τ TF q σ A. D. Becke and K. E. Edgecombe, J. Chem. Phys. 92, 5397 (1990). Physical meaning : C ∈ [0 : 1] C q σ ( r ) = 1 Probability to find another particle with the same q and σ very low. C q σ ( r ) = 0 . 5 Limit of uniform-density Fermi gas. Mask function : → C q σ ( r ) ρ q σ ρ max q σ P. Jerabek, B. Schuetrumpf, P. Schwerdtfeger, and W. Nazarewicz, Phys. Rev. Lett. 120 , 053001 (2018).

Nucleon localization function Fermion localization function � 2 � − 1 Schematic system � 4 |∇ ρ q σ | 2 − j 2 � τ q σ ρ q σ − 1 q σ C q σ ( r ) = 1 + ρ q σ τ TF q σ A. D. Becke and K. E. Edgecombe, J. Chem. Phys. 92, 5397 (1990). Physical meaning : C ∈ [0 : 1] C q σ ( r ) = 1 Probability to find another particle with the same q and σ very low. C q σ ( r ) = 0 . 5 Limit of uniform-density Fermi gas. Mask function : → C q σ ( r ) ρ q σ ρ max q σ

Example of 240 Pu 240 Pu

Example of 240 Pu 240 Pu

Example of 240 Pu 240 Pu

Example of 240 Pu 240 Pu

Example of 240 Pu Hypothesis The octupole shell effects are important in the fission fragment

Other systems

Other systems

Other systems

Why the fragments have octupole deformation ? Similar effect on fusion reaction 40 Ca+ 40 Ca, E 3 − = 3.7 MeV 56 Ni+ 56 Ni, E 3 − = 7.5 MeV C. Simenel, M. Dasgupta, D. J. Hinde, and E. Williams, Phys. Rev. C 88, 064604 (2013).

Why the fragments have octupole deformation ? Similar effect on fusion reaction 40 Ca+ 40 Ca, E 3 − = 3.7 MeV 56 Ni+ 56 Ni, E 3 − = 7.5 MeV C. Simenel, M. Dasgupta, D. J. Hinde, and E. Williams, Phys. Rev. C 88, 064604 (2013).

Octupole deformation systematics Skyrme Skm*. Gogny D1S LM Robledo - J. phys. G : Nucl. and S. Ebata, and T. Nakatsukasa, Phys. Scr. Particle Physics, 2015 92 (2017) 064005 Results from systematic calculation In both calculations, the region Z ≃ 54 , N ≃ 88 is favorable for octupole deformation . Experimental results 144 Ba is found to be octupole in its groud state. Bucher et al. PRL 116 (2016).

Constraint HF+BCS octupole deformation with Sly4d Result from constraint calculation of the heavy fragment The gain in energy due to the octupole softness drives the fission to the Z ≃ 54

Structure, 144 Ba, Z=56, N=88 Single particle energy Q 30 [b 3 / 2 ] 0 0 0 2 3 4 5 -2 -3 -4 Q 2 - Q 3 potential energy surface -5 ǫ n [MeV] 88 -6 -7 82 84 -8 -9 -10 0.0 0.5 1.0 1.5 2.0 2.5 3 4 5 6 Q 20 [b] Q 30 [b 3 / 2 ] 0 0 0 2 3 4 5 -7 -8 -9 -10 56 -11 ǫ p [MeV] -12 -13 50 52 -14 -15 -16 -17 0.0 0.5 1.0 1.5 2.0 2.5 3 4 5 6 Q 20 [b]

Conclusion Mechanism The Nucleus-Nucleus interaction at the scission configuration favors the octupole shapes Shell structure favors octupole shape in the region Z ≃ 52-56, N ≃ 84-88 Actinide fission fragments are driven in the region Z ≃ 54, N ≃ 86 G. Scamps, C. Simenel, Nature 564, 382 (2018).

Similar effect for other systems ? P. A. Butler,

Experimental data of 180 Hg A. N. Andreyev, et al., PRL 105, 252502 (2010)

Experimental data of 178 Pt I. Tsekhanovich, ArXiv :1804.01832

Similar effect of the octupole deformation ?

CHF+BCS calculation C n 0.5 0.4 0.3 0.2 0.1 0.0 - 10 -5 y [fm] 0 5 1 0 0 R u 8 0 K r 10 -20 -15 -10 -5 0 5 10 15 20 z [fm]

Comparison with experimental data Experimental article : A. N. Andreyev, C n et al. Phys. Rev. Lett. 105, 252502 0.5 0.4 (2010). 0.3 0.2 0.1 0.0 - 10 -5 y [fm] 0 5 1 0 0 R u 8 0 K r 10 -20 -15 -10 -5 0 5 10 15 20 z [fm]

Single particle energies Structure of 100 Ru (Z=44 and N=56) Structure of 80 Kr (Z=36 and N=44) β 3 β 3 = 0 β 2 = 0.75 0 0 0 0.2 0.3 0.4 0.5 -5 -5 -6 -6 50 -7 -7 -8 -8 56 ǫ n [MeV] ǫ n [MeV] -9 -9 44 -10 -10 52 -11 -11 50 -12 -12 38 -13 -13 36 -14 -14 -5 -2 -6 -4 50 -7 -8 36 -6 ǫ p [MeV] ǫ p [MeV] -9 44 32 -8 -10 -11 -10 -12 28 -13 34 -12 -14 0.0 0.2 0.4 0.6 0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 β 2 β 2 β 3

180 Hg 178 Pt 60 80 100 120 A 60 80 100 120 A Protons N=56 198 Hg N=52 N=50 Z=50 50 75 100 125 150 A 190 Hg N=82 Z=36 50 75 100 125 150 A Neutrons Z=28 G. Scamps and C. Simenel, arXiv :1904.01275

CHF+BCS calculations : Hg isotopic chain -1375 Symmetric 178 Hg Z=46 178 Hg -1380 Asymmetric N=56 E [MeV] Z=34 -1385 N=42 -1390 -1400 180 Hg Z=44 180 Hg N=56 Z=36 N=44 E [MeV] -1405 -1410 Z=44 182 Hg N=56 182 Hg Z=36 -1420 N=46 E [MeV] C n -1425 0.5 Z=44 184 Hg 0.4 N=57 -1430 -1435 0.3 Z=36 184 Hg N=47 0.2 -1440 0.1 E [MeV] Z=43 0.0 186 Hg N=57 -1445 Z=37 N=49 -1450 186 Hg -1455 E [MeV] Z=45 188 Hg -1460 N=62 Z=35 -1465 N=46 -1470 188 Hg Z=40 188 Hg -1475 E [MeV] N=54 Sym. -1480 -1485 0 20 40 60 80 100 120 Q 20 [b]

Preliminary results for 188 Pb with Sly4d and BCS 50 -1460 188 Pb 188 Pb 45 A H =102 40 35 -1465 A H =100 E [MeV] 30 Q 30 [b] 25 20 -1470 15 10 A H =96 5 A H =94 0 -1475 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 Q 20 [b 3 / 2 ] Q 20 []

Preliminary results for 188 Pb with Sly4 and Constrained Hartree-Fock + BCS 50 -1445 188 Pb 188 Pb 45 -1450 40 A H =107 35 -1455 A H =103 E [MeV] Q 30 [b 3 / 2 ] 30 25 -1460 20 -1465 15 10 -1470 5 A H =94 0 -1475 0 20 40 60 80 100 120 140 160 0 20 40 60 80 100 120 140 Q 20 [b] Q 20 [b]

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