Role of fission in r -process nucleosynthesis Samuel A. Giuliani - PowerPoint PPT Presentation

Role of fission in r -process nucleosynthesis Samuel A. Giuliani NSCL/FRIB, East Lansing July 12th, 2018 FRIB and the GW170817 kilonova NSCL/FRIB at MSU

Introduction Fission and r process Fission fragments distributions Conclusions & Outlook Outline 1. Introduction 2. Impact of fission on r -process nucleosynthesis 3. Fission fragments distributions 4. Conclusions & Outlook

Introduction Fission and r process Fission fragments distributions Conclusions & Outlook Outline 1. Introduction 2. Impact of fission on r -process nucleosynthesis 3. Fission fragments distributions 4. Conclusions & Outlook

Introduction Fission and r process Fission fragments distributions Conclusions & Outlook The r process r (apid neutron capture) process: τ n ≪ τ β − β decay neutron capture unstable nuclei stable nuclei Z neutron N shell closure How far can the r process proceed? Number of free neutrons that seed nuclei can capture (neutron-to-seed ratio).

Introduction Fission and r process Fission fragments distributions Conclusions & Outlook r process and fission 250 Solar r abundances Known mass Known half − life r − process waiting point (ETFSI − Q) 200 100 98 f i s s i o n 96 94 92 90 88 86 188 190 84 186 82 80 78 184 180 182 150 76 178 176 74 164 166 168 170 172 174 N=184 162 72 160 70 68 158 66 156 154 64 152 150 62 140 142 144 146 148 For large neutron-to-seed ratio 1 10 60 138 134 136 130 132 0 58 128 10 56 − 1 54 126 fission is unavoidable 124 10 52 122 − 2 120 50 100 116 118 10 N=126 − 3 48 112 114 110 10 46 108 106 104 44 - n -induced fission 100 102 98 42 96 40 92 94 38 88 90 86 36 84 82 34 80 78 - β -delayed fission 32 74 76 72 30 N=82 70 66 68 28 64 26 62 28 60 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 - spontaneous fission ◮ Where does fission occur? ◮ How much material accumulates in fissioning region? ◮ What are the fission yields?

Introduction Fission and r process Fission fragments distributions Conclusions & Outlook 1) Compute fission properties and binding energies using BCPM EDF. B f − S n (MeV) -2 0 2 4 6 8 10 12 14 120 Proton number 110 Sn = 2 MeV 100 Sn = 0 MeV 90 120 140 160 180 200 220 240 Neutron number 2) Calculate stellar reaction rates from Hauser-Feshbach theory. Dominating channel at n n =10 28 cm − 3 120 (n, γ ) Proton number 110 (n,fission) spont. fission 100 Sn= 2 MeV Sn= 0 MeV 90 120 140 160 180 200 220 240 Neutron number 3) Obtain r -process abundances using network calculations. log 10 (Y) -25 -20 -15 -10 -5 0 120 Proton number 110 100 90 120 140 160 180 200 220 240 Neutron number

Introduction Fission and r process Fission fragments distributions Conclusions & Outlook The fission process -2035 neutron-induced inner beta-delayed barrier outer photo-induced barrier E * fission -2040 E HFB (MeV) ground fission spontaneous state isomer fission -2045 286 Fl -2050 114 0 10 20 30 40 50 60 70 80 Q 20 (b) Potential Energy Surface Collective inertias Energy evolution from the initial Resistance of the nucleus state to the scission point. against the deformation forces. SAG+ PRC90(2014); Sadhukhan+ PRC90(2014) Baran+ PRC84 (2011)

Introduction Fission and r process Fission fragments distributions Conclusions & Outlook The Hartree-Fock-Bogolyubov (HFB) formalism The ground-state wavefunction is obtained by minimizing the total energy: δ E [ | Ψ � ] = 0 , where | Ψ � is a quasiparticle ( β ) vacuum: � | Ψ � = β µ | 0 � ⇒ β µ | Ψ � = 0 . µ The energy landscape is constructed by constraining the deformation of the nucleus � Ψ( q ) | ˆ Q | Ψ( q ) � = q : E [ | Ψ( q ) � ] = � Ψ( q ) | ˆ H − λ q ˆ Q | Ψ( q ) � . The energy density functionals (EDF) provide a phenomenological ansatz of the effective nucleon-nucleon interaction: - Barcelona-Catania-Paris-Madrid (BCPM); - Skyrme and Gogny interactions (UNEDF1, D1S); - relativistic EDF.

Introduction Fission and r process Fission fragments distributions Conclusions & Outlook Outline 1. Introduction 2. Impact of fission on r -process nucleosynthesis 3. Fission fragments distributions 4. Conclusions & Outlook

Introduction Fission and r process Fission fragments distributions Conclusions & Outlook Nuclear inputs from the BCPM EDF We study the impact of fission in the r process by comparing BCPM with previous calculations based on Thomas-Fermi (TF) barriers and Finite Range Droplet Model (FRDM) masses. Fission barrier (MeV) 0 2 4 6 8 10 12 14 120 18 BCPM BCPM Proton number 126 110 14 S 2 n (MeV) Sn = 2 MeV 10 100 Sn = 0 MeV 6 174 90 2 184 120 18 TF FRDM Proton number 126 110 14 S 2 n (MeV) 10 100 6 174 90 2 184 120 140 160 180 200 220 240 90 100 110 120 Neutron number Proton number BCPM : Giuliani et al. (2018); TF : Myers and ´ Swiat ¸ecky (1999); FRDM : M¨ oller et al. (1995).

Introduction Fission and r process Fission fragments distributions Conclusions & Outlook Compound reactions Reaction rates computed within the Hauser-Feshbach statistical model. γ gamma decay particle emission compound target nucleus fission - Based on the Bohr independence hypothesis: the decay of the compound nucleus is independent from its formation dynamics. - BCPM nuclear inputs implemented in TALYS reaction code to compute n -induced fission and n -capture rates.

Introduction Fission and r process Fission fragments distributions Conclusions & Outlook Cross sections from BCPM 10 4 10 3 σ ( n,fiss ) (mb) 10 2 Experiment 10 1 BCPM 235U(n,fis) 238U(n,fis) 238Pu(n,fis) 10 4 Energy (MeV) Energy (MeV) Energy (MeV) 235U(n,g) 238U(n,g) 238Pu(n,g) 10 3 σ ( n,γ ) (mb) 10 2 10 1 10 -2 10 -1 10 0 10 1 10 -2 10 -1 10 0 10 1 10 -2 10 -1 10 0 10 1 Energy (MeV) Energy (MeV) Energy (MeV)

Introduction Fission and r process Fission fragments distributions Conclusions & Outlook Stellar reaction rates - impact of collective inertias? spont. fis. ( n , γ ) ( n ,fis) α -decay ( n , 2 n ) ( n , α ) 120 110 100 ATDHFB-r 90 120 Proton number 110 Sn = 2 MeV 100 Sn = 0 MeV GCM-r 90 120 110 100 SEMP-r 90 120 140 160 180 200 220 240 Neutron number SAG, Mart´ ınez-Pinedo and Robledo, Phys. Rev. C 97, 034323 (2018)

Introduction Fission and r process Fission fragments distributions Conclusions & Outlook The dynamical ejecta in neutron mergers Trajectory from 3D relativistic simulations of 1 . 35 M ⊙ - 1 . 35 M ⊙ NS mergers. 30 14.5 30 14.5 14 14 20 20 13.5 13.5 13 13 10 10 12.5 12.5 12 12 y [km] y [km] 0 0 11.5 11.5 11 11 10 10 10.5 10.5 10 10 20 20 9.5 9.5 30 30 9 9 30 20 10 0 10 20 30 30 20 10 0 10 20 30 x [km] x [km] 13.0056 ms 13.4824 ms 50 14.5 50 14.5 14 14 40 40 13.5 13.5 30 30 13 13 20 20 12.5 12.5 10 10 y [km] 12 y [km] 12 0 0 11.5 11.5 10 10 11 11 20 20 10.5 10.5 30 30 10 10 40 40 9.5 9.5 50 50 9 9 50 0 50 50 0 50 x [km] x [km] 13.8024 ms 15.167 ms Bauswein et al., ApJ 773, 78 (2013). - Large amount of ejecta ( 0 . 001 - 0 . 01 M ⊙ ). - Material extremely neutron rich ( R n / s � 600 ). - Role of weak interactions?

Introduction Fission and r process Fission fragments distributions Conclusions & Outlook r -process abundances: BCPM vs FRDM+TF -2 10 abundances at n/s=1 -3 10 ◮ Trajectory: 3D relativistic simulations from -4 10 1 . 35 M ⊙ - 1 . 35 M ⊙ NS mergers [Bauswein+(2013)] . -5 10 -6 10 ◮ BCPM Giuliani+(2017) vs TF+FRDM Panov+(2010) . -7 10 ◮ We changed the rates of nuclei with Z ≥ 84 . -8 10 -9 10 ◮ Same β -decay rates [M¨ oller et al. PRC67(2003)] . -2 10 abundances at τ (n, γ ) = τ β -3 10 -4 10 -5 10 -6 10 -7 10 -8 10 -9 10 -2 10 abundances at 1 Gyr -3 10 -4 10 -5 10 -6 10 solar -7 10 BCPM -8 10 FRDM+ TF -9 10 100 150 200 250 300 A

Introduction Fission and r process Fission fragments distributions Conclusions & Outlook r -process abundances: BCPM vs FRDM+TF -2 10 abundances at n/s=1 ◮ Trajectory: 3D relativistic simulations from -3 10 -4 10 1 . 35 M ⊙ - 1 . 35 M ⊙ NS mergers [Bauswein+(2013)] . -5 10 ◮ BCPM Giuliani+(2017) vs TF+FRDM Panov+(2010) . -6 10 -7 10 ◮ We changed the rates of nuclei with Z ≥ 84 . -8 10 ◮ Same β -decay rates [M¨ -9 oller et al. PRC67(2003)] . 10 -2 10 abundances at τ (n, γ ) = τ β -3 10 ◮ BCPM barriers larger than TF: -4 10 -5 10 - nuclei around A > 280 longer lifetimes , -6 10 - accumulation above 2 nd peak. -7 10 -8 10 ◮ BCPM shell gap smaller than FRDM at N = 174 : -9 10 -2 10 abundances at 1 Gyr - FRDM-TF peak at A ∼ 257 , -3 10 -4 10 - impact on final abundances at A ∼ 110 . -5 10 -6 10 ◮ Same 232 Th/ 238 U ratio: progenitors of actinides solar -7 10 BCPM have Z < 84 ⇒ can initial nuclei with Z ≥ 84 -8 10 FRDM+ TF -9 survive to fission? 10 100 150 200 250 300 A