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: τn τβ− 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 Known mass Known half−life r−process waiting point (ETFSI−Q) 100 200 98 96 94 92 fission 90 88 Solar r abundances 86 84 188 190 186 82 80 78 184 180 182 76 178 176 74 164 166 168 170 172 174 150 72 162 70 160 N=184 68 158 66 156 154 64 152 150 62 140 142 144 146 148 1 60 138 134 136 58 130 132 For large neutron-to-seed ratio 0 128 10 56 54 126 10 −1 124 52 122 120 50 116 118 fission is unavoidable 10 −2 48 112 114 110 10 46 −3 108 N=126 100 106 44 104 100 102 42 10 98 96 40 92 94 - n-induced fission 38 88 90 86 36 84 82 34 80 78 32 74 76 30 72 70 - β-delayed fission 28 66 68 64 26 62 N=82 28 60 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 - spontaneous fission I Where does fission occur? I How much material accumulates in fissioning region? I 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. Bf −Sn (MeV) -2 0 2 4 6 8 10 12 14 120 110 Sn = 2 MeV 100 Sn = 0 MeV 90 Protonnumber 120 140 160 180 200 220 240 Neutron number 2) Calculate stellar reaction rates from Hauser-Feshbach theory. 28 3 Dominating channel at n =10 cm− 120 n (n,γ) 110 (n,fission) spont. fission 100 Sn= 2 MeV Sn= 0 MeV 90 Proton number 120 140 160 180 200 220 240 Neutron number 3) Obtain r-process abundances using network calculations. log10(Y) -25 -20 -15 -10 -5 0 120 110 100 90 Proton number 120 140 160 180 200 220 240 Neutron number Introduction Fission and r process Fission fragments distributions Conclusions & Outlook The fission process -2035 inner neutron-induced barrier outer beta-delayed photo-induced * barrier E fission -2040 (MeV) ground fission spontaneous state isomer fission HFB -2045 E 286 -2050 114Fl 0 10 20 30 40 50 60 70 80 Q20 (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: δE[|Ψi] = 0 , where |Ψi is a quasiparticle (β) vacuum: Y |Ψi = βµ|0i ⇒ βµ|Ψi = 0 . µ The energy landscape is constructed by constraining the deformation of the nucleus hΨ(q)|Qˆ |Ψ(q)i = q: E[|Ψ(q)i] = hΨ(q)|Hˆ − λqQˆ |Ψ(q)i . 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 BCPM 18 BCPM 126 110 14 Sn = 2 MeV 10 100 Sn = 0 MeV (MeV) n 2 6 174 S 90 Proton number 2 184 120 TF 18 FRDM 126 110 14 100 10 (MeV) n 2 6 174 S 90 Proton number 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 target compound 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 104 103 (mb) ) 102 n,fiss ( σ 101 Experiment BCPM 235U(n,fis) 238U(n,fis) 238Pu(n,fis) 104 Energy (MeV) Energy (MeV) Energy (MeV) 235U(n,g) 238U(n,g) 238Pu(n,g) 103 (mb) 2 ) 10 n,γ ( σ 101 10-2 10-1 100 101 10-2 10-1 100 101 10-2 10-1 100 101 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,α) (n,2n) 120 110 100 90 ATDHFB-r 120 110 Sn = 2 MeV 100 Sn = 0 MeV 90 GCM-r Proton number 120 110 100 90 SEMP-r 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 13.5 20 13.5 13 13 10 10 12.5 12.5 12 12 0 0 y [km] y y [km] y 11.5 11.5 11 11 10 10 10.5 10.5 20 10 20 10 9.5 9.5 30 9 30 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 40 14 40 13.5 30 13.5 30 13 13 20 20 12.5 12.5 10 10 12 12 0 0 y [km] y y [km] y 11.5 11.5 10 10 11 11 20 20 10.5 10.5 30 30 10 10 40 9.5 40 9.5 50 9 50 9 50 0 50 50 0 50 x [km] 13.8024 ms x [km] 15.167 ms Bauswein et al., ApJ 773, 78 (2013). - Large amount of ejecta (0.001-0.01 M ). - Material extremely neutron rich (Rn/s & 600). - Role of weak interactions? - nuclei around A > 280 longer lifetimes , - accumulation above 2nd peak. - FRDM-TF peak at A ∼ 257, - impact on final abundances at A ∼ 110. I BCPM barriers larger thanTF: I BCPM shell gap smaller than FRDM at N = 174: I Same 232Th/238U ratio: progenitors of actinides have Z < 84 ⇒ can initial nuclei with Z ≥ 84 survive to fission? Introduction Fission and r process Fission fragments distributions Conclusions & Outlook r-process abundances: BCPM vs FRDM+TF 10-2 abundances at n/s=1 10-3 I Trajectory: 3D relativistic simulations from 10-4 1.35 M -1.35 M NS mergers [Bauswein+(2013)]. 10-5 10-6 BCPM Giuliani+(2017) vs TF+FRDM Panov+(2010). I 10-7 I We changed the rates of nuclei with Z ≥ 84. 10-8 10-9 -2 Same β-decay rates [M¨oller et al. PRC67(2003)]. 10 I abundances at τ (n,γ) = τβ 10-3 10-4 10-5 10-6 10-7 10-8 10-9 10-2 abundances at 1 Gyr 10-3 10-4 10-5 10-6 10-7 solar BCPM 10-8 FRDM+ TF 10-9 100 150 200 250 300 A Introduction Fission and r process Fission fragments distributions Conclusions & Outlook r-process abundances: BCPM vs FRDM+TF 10-2 abundances at n/s=1 I Trajectory: 3D relativistic simulations from 10-3 10-4 1.35 M -1.35 M NS mergers [Bauswein+(2013)]. 10-5 I BCPM Giuliani+(2017) vs TF+FRDM Panov+(2010). 10-6 10-7 We changed the rates of nuclei with Z ≥ 84. -8 I 10 -9 Same β-decay rates [M¨oller et al. PRC67(2003)]. 10 I 10-2 abundances at τ (n,γ) = τβ 10-3 I BCPM barriers larger thanTF: 10-4 -5 - nuclei around A > 280 longer lifetimes , 10 10-6 - accumulation above 2nd peak. 10-7 10-8 I BCPM shell gap smaller than FRDM at N = 174: 10-9 10-2 abundances at 1 Gyr - FRDM-TF peak at A ∼ 257, 10-3 - impact on final abundances at A ∼ 110.