Impact of fission on r-process nucleosynthesis within the energy density functional theory

Transcription

1 Impact of fission on r-process nucleosynthesis within the energy density functional theory Samuel A. Giuliani, G. Martínez Pinedo, L. M. Robledo, M.-R. Wu Technische Universität Darmstadt, Darmstadt, Germany Universidad Autónoma de Madrid, Madrid, Spain January 17th, 017 Neutron star mergers: from gravitational waves to nucleosynthesis Hirschegg, Austria

2 Outline 1. Introduction r-process in neutron star mergers (NSM). Fission rates from the BCPM EDF Fission within the Energy Density Functional approach Fission properties of the BCPM EDF Stellar reaction rates 3. r-process nucleosynthesis in NSM r-process abundances: BCPM vs FRDM-TF Radioactivity Averaged fission rates. Conclusions & Outlook

3 Outline 1. Introduction r-process in neutron star mergers (NSM). Fission rates from the BCPM EDF Fission within the Energy Density Functional approach Fission properties of the BCPM EDF Stellar reaction rates 3. r-process nucleosynthesis in NSM r-process abundances: BCPM vs FRDM-TF Radioactivity Averaged fission rates. Conclusions & Outlook

4 r-process abundances distributions Cowan & Sneden, Nature 0, 1151 (00). 0 Relative log ε 10 1 CS9 05 HD115 BD Atomic number Site? CS HD1170 SS r-process abundances

5 r-process in Neutron Star Mergers & fission Solar r abundances N= Known mass Known half life r process waiting point (ETFSI Q) N=1 r process path N= fission recycling Mendoza-Temis et al., Phys. Rev. C9, (015) Condition for robust r-process abundances in NSM Material in the fissioning region (A > 50) dominating at freeze-out systematic calculations of fission rates using different models are required!

6 Outline 1. Introduction r-process in neutron star mergers (NSM). Fission rates from the BCPM EDF Fission within the Energy Density Functional approach Fission properties of the BCPM EDF Stellar reaction rates 3. r-process nucleosynthesis in NSM r-process abundances: BCPM vs FRDM-TF Radioactivity Averaged fission rates. Conclusions & Outlook

7 Fission within the Energy Density Functional approach Potential Energy Surface Energy evolution from the ground state to the scission point. Relevant degrees of freedom? SAG+ PRC90(01); Sadhukhan+ PRC90(01) Collective inertias Resistance of the nucleus against the deformation forces. Hard to compute. Baran+ PRC (011) Fl -0 E(Q 0 ) [MeV] Q 0 [b]

8 Static fission properties Parameters defining the potential energy surface: - inner and outer fission barrier heights, - isomer excitation energy. Probability of tunneling under the fission barrier (WKB): 1 P = 1 + exp(s) ; S = b a ( dq 0 [ B(Q 0 ) V (Q0 ) E )] 1. } {{ }} {{ } inertias PES - Spontaneous fission lifetimes: t sf = ln n P ; - fission cross sections. Interaction: - Now: Barcelona-Catania-Paris-Madrid EDF Baldo et al., PRC7 (013). - (next) Future: Gogny and BCPM EDFs.

9 Proton number BCPM: systematic of fission barriers 10 BCPM TF HFB1 110 Sn = MeV 100 Sn = 0 MeV 1 10 Fission barrier (MeV) Neutron number Mean-field models predict larger B f than mic-mac for Z 110; BCPM: SG, Martínez-Pinedo and Robledo (in preparation); HFB1: S. Goriely et al., PRC75 (007); TF: W. D. Myers and W. J. Swiatecki, PRC0 (1999); FRDM: P. Möller et al., At. Data Nucl. Data Tables 5 (1995).

10 BCPM: systematic of fission barriers 10 BCPM 110 B f S n (MeV) Proton number HFB1 110 Sn = MeV 100 Sn = 0 MeV TF-FRDM Neutron number 0 Mean-field models predict larger B f than mic-mac for Z 110; n-induced fission important above N = 1. BCPM: SG, Martínez-Pinedo and Robledo (in preparation); HFB1: S. Goriely et al., PRC75 (007); TF: W. D. Myers and W. J. Swiatecki, PRC0 (1999); FRDM: P. Möller et al., At. Data Nucl. Data Tables 5 (1995).

11 Nuclear inputs for reaction rates Reaction rates require knowledge/modeling of nuclear level densities, γ-ray strengths, masses, fission barriers... The EDF theory useful framework for providing nuclear inputs: Sn - neutron separation energies and barriers from the same interaction; BCPM Z = Z = N Sn FRDM Z = Z = N - tunneling probability from full fission barrier and microscopic collective inertias. Several optical models, level densities and γ-ray strengths implemented in TALYS.

12 Introduction Fission rates from the BCPM EDF r-process nucleosynthesis in NSM Conclusions & Outlook Cross sections: BCPM vs experiment I n-induced fission, γ-induced fission, spontaneous fission and n-capture rates computed using the BCPM nuclear masses and fission barriers. σ(n,fiss) (mb) 10 39Pu 0Pu 1Pu σ(n,fiss) (mb) 3Pu Experiment Constant Temperature Back-Shifted Fermi Gas Energy (MeV) Energy (MeV) 101

13 Cross sections: BCPM vs experiment n-induced fission, γ-induced fission, spontaneous fission and n-capture rates computed using the BCPM nuclear masses and fission barriers [mb] n,f 3 Pu(n,f) 39 Pu(n,f) Pu(n,f) 1 Pu(n,f) E [MeV] E [MeV] E [MeV] E [MeV] Goriely, Eur. Phys. J. A (015) 51:.

14 Outline 1. Introduction r-process in neutron star mergers (NSM). Fission rates from the BCPM EDF Fission within the Energy Density Functional approach Fission properties of the BCPM EDF Stellar reaction rates 3. r-process nucleosynthesis in NSM r-process abundances: BCPM vs FRDM-TF Radioactivity Averaged fission rates. Conclusions & Outlook

15 Introduction r-process nucleosynthesis in NSM Fission rates from the BCPM EDF Conclusions & Outlook BCPM rates log10(y) Proton number Neutron number Dominating channel at nn 10 Proton number -0 = cm (n,γ) (n,fission) spont. fission Sn= MeV Sn= 0 MeV Neutron number 0 0 I Narrow (n, γ) path through A 300; r-path up to A 30. I Fission dominates at A & 350: heavier nuclei cannot be produced. I SF relevant when Bf < MeV.

16 r-process abundances: BCPM vs FRDM-TF Panov+, A&A 513 (010) Trajectory: 3D relativistic simulations from 1.35 M M NS mergers [Bauswein+(013)]. Same rates for Z 3 and same τ β. abundances at n/s=1 abundances at τ (n,γ) =τ β abundances at 1 Gy PANOV BCPM solar A

17 r-process abundances: BCPM vs FRDM-TF Panov+, A&A 513 (010) Trajectory: 3D relativistic simulations from 1.35 M M NS mergers [Bauswein+(013)]. Same rates for Z 3 and same τ β. Bf BCPM > Bf TF and BCPM n > FRDM n at N = 1: larger production of nuclei with A > 0. abundances at n/s=1 abundances at τ (n,γ) =τ β abundances at 1 Gy PANOV BCPM solar A

18 r-process abundances: BCPM vs FRDM-TF Panov+, A&A 513 (010) Trajectory: 3D relativistic simulations from 1.35 M M NS mergers [Bauswein+(013)]. Same rates for Z 3 and same τ β. Bf BCPM > Bf TF and BCPM n > FRDM n at N = 1: larger production of nuclei with A > 0. Accumulation above the nd peak: abundances at n/s=1 abundances at τ (n,γ) =τ β abundances at 1 Gy PANOV BCPM solar A

19 r-process abundances: BCPM vs FRDM-TF Panov+, A&A 513 (010) Trajectory: 3D relativistic simulations from 1.35 M M NS mergers [Bauswein+(013)]. Same rates for Z 3 and same τ β. Bf BCPM > Bf TF and BCPM n > FRDM n at N = 1: larger production of nuclei with A > 0. Accumulation above the nd peak: - formed by fission fragments of nuclei with A 3. abundances at n/s=1 abundances at τ (n,γ) =τ β abundances at 1 Gy PANOV BCPM solar A

20 r-process abundances: BCPM vs FRDM-TF Panov+, A&A 513 (010) Trajectory: 3D relativistic simulations from 1.35 M M NS mergers [Bauswein+(013)]. Same rates for Z 3 and same τ β. Bf BCPM > Bf TF and BCPM n > FRDM n at N = 1: larger production of nuclei with A > 0. Accumulation above the nd peak: - formed by fission fragments of nuclei with A 3. FRDM-TF peak at A 57: - jump in S n at N = 17 (not present in BCPM). abundances at n/s=1 abundances at τ (n,γ) =τ β abundances at 1 Gy PANOV BCPM solar A

21 r-process abundances: BCPM vs FRDM-TF Panov+, A&A 513 (010) Trajectory: 3D relativistic simulations from 1.35 M M NS mergers [Bauswein+(013)]. Same rates for Z 3 and same τ β. Bf BCPM > Bf TF and BCPM n > FRDM n at N = 1: larger production of nuclei with A > 0. Accumulation above the nd peak: - formed by fission fragments of nuclei with A 3. FRDM-TF peak at A 57: - jump in S n at N = 17 (not present in BCPM). Similar 3Th/3U ratio: relevant physics below Z = or close to stability. abundances at n/s=1 abundances at τ (n,γ) =τ β abundances at 1 Gy PANOV BCPM solar A

22 Emitted radioactive energy Energy emitted by radioactive products in NSM crucial for predicting kilonova light curves [J. Barnes et al., ApJ (01)] Fraction of radioactive energy 10-1 BCPM Panov β-decay α-decay total fission Days Minor impact in the radioactive energy production physics Z < and/or β-decay more relevant.

23 Averaged fission rates BCPM Panov n-induced fission β-delayed fission spontan. fission γ-induced fission Rate (s 1 ) Time (s) n-induced dominates until freeze-out and revived by β-delayed neutrons β-delayed fission rates from BCPM barriers required! photo-induced fission always subdominant; decay of material to stability triggers spontaneous fission.

24 Introduction r-process nucleosynthesis in NSM Fission rates from the BCPM EDF Conclusions & Outlook What is next? Gogny interaction Fission barrier (MeV) D1M-BCPM Sn = MeV Sn = 0 MeV D1S-BCPM 10 D1M-BCPM Neutron number Neutron number 0 I Three Gogny parametrizations in the market: D1S, D1M, D1N. I BCPM and Gogny differ up to 5 MeV for r-process nuclei: impact in rates/abundances? Proton number Proton number D1M D1S 110 Sn = MeV 100 Sn = 0 MeV D1N Fission barrier: GOGNY vs BCPM (MeV) 0

25 Outline 1. Introduction r-process in neutron star mergers (NSM). Fission rates from the BCPM EDF Fission within the Energy Density Functional approach Fission properties of the BCPM EDF Stellar reaction rates 3. r-process nucleosynthesis in NSM r-process abundances: BCPM vs FRDM-TF Radioactivity Averaged fission rates. Conclusions & Outlook

26 Conclusions Fission plays a crucial role in r-process nucleosynthesis. EDFs valuable tool for a microscopic description of the fission process. New set of stellar rates suited for r-process calculations using the BCPM EDF: - n-induced, γ-induced fission and spontaneous fission stellar rates. BCPM fission barriers higher than TF: r-process towards A 30. Small impact on radioactive energy generation and 3Th/3U ratio. Future work: - computation of fragments distributions; - β-delayed fission rates; - explore sensitivity to BCPM and different EDF s (Gogny, BCPM ).

27 Thank you!

28 Minimizing the action: B( N ) vs E( N ) - 3 U E rot (MeV) S = b a ds B(s) [ ] E(s) E 0 B 1/ N E rot N action S.00e e e e e e e e e-0.90e e-0.9e-03.00e-03.9e-03.00e-03.9e-03.00e-03.09e e N S ( h) B ( h /MeVb )

29 The least action path The least action path (black) strongly differ from the least energy one (red)!

30 Fission barriers and E 0 - U E HFB E GS (MeV) S = b U a ds B(s) [ ] E(s) E 0 STATIC DYNAMIC Q (b)

31 Spontaneous fission lifetimes (BCPM results) Exp: Xiaojun Bao et al., Nucl. Phys. A90, 1 13 (013). log 10 (t SF [s]) Th 3U 3U 3U 35U 3U 50Cm Cm Cm Cm 5Cm Cm 3Cm 0Cm No 0No 5No 5No 5No 5No 50No 3Am 5Cf 1Am 5Cf 5Cf 50Cf Cf 9Cf Cf Cf 0Cf 3Cf 7Md 5Md 3Db 0Db 57Db 55Db 39Pu Pu Pu 0Pu 3Pu 3Pu 9Bk 59Fm 57Fm 55Fm 0Fm 5Fm 5Fm 5Fm 5Fm 50Fm Fm Fm Fm ZZ /AA 3Fm 1Fm 53Es 55Es Lr 5Lr 1Lr 59Lr Rf 0Rf ATDHFB GOA-GCM SEMP EXP 59Rf 57Rf 55Rf 53Rf 5Rf 5Rf 5Rf 0Sg 5Sg Hs ZZ /AA

32 BCPM barrier heights and isomer energy Exp:R. Capote et al., Nucl. Data Sheets 110, 3107 (009); S. Bjørnholm and J. E. Lynn, Rev. Mod. Phys. 5, 75 (190). B I B II E II BCPM-EXPERIMENT (MeV) N Bjørnholm Capote N N 0

33 BCPM barrier heights and isomer energy BCPM: Baldo et al., PRC7 (013) Exp: Sing et al., Nucl. Data Sheets 97, 1 (00); R. Capote et al., Nucl. Data Sheets 110, 3107 (009). E [MeV] U 3U Potential energy surface parameters 3U 3Pu 0Pu Pu Pu 0Cm Cm Cm Cm Cm 50Cf 5Cf Inner barrier Isomer excitation Outer barrier EXP BCPM SAG and Robledo, Phys. Rev. C, 0535 (013) - Outer barriers and isomer energies quite well reproduced for all nuclei. - Inner barriers are reduced when triaxiality is allowed (Erler+(01), Guzmán+(01)).

34 Uranium fission barrier heights: theoretical predictions Fission barriers heights [MeV] BSk1: S. Goriely et al., Phys. Rev. C75, 031 (007). Möller: P. Möller et al., Phys. Rev. C91, 0310 (015). Experimental Moeller BSk1 BCPM Z=9 log 10 (t sf (s)) Experimental BSk1 BCPM Z= N BSk1: 0 Collective inertias B = 0.05A 5/3 MeV 1 BCPM: B = 1 (M ) with M (M 1) 3 ( n) = N α>β αβ Q 0 0 (E α + E β ) n

35 The BCPM functional The energy of a finite nucleus is given by E = T 0 + Eint + Eint FR E int[ρ p, ρ n] = + E s.o. + E C + E pair d r [ P s(ρ)(1 β ) + P n(ρ)β ] ρ with ρ( r) = ρ n( r) + ρ p( r) and β( r) = (ρ n( r) ρ p( r))/ρ( r). P s and P n are polynomial fits to reproduce microscopic EoS in nuclear matter. Phenomenological surface contribution Eint FR [ρ n, ρ p] = 1 d rd r ρ t( r)v t,t ( r r )ρ t ( r ) t,t with v t,t (r) = V t,t e r /r 0 tt ; Vn,n = V p,p = V L = b 1/(π 3/ r 3 0Lρ 0); V n,p = V p,n = V U = (a 1 b 1)/(π 3/ r 3 0Uρ 0). M.Baldo et al. Phys. Lett. B3 (00) 390; Phys. Rev. C (013)

36 Remaining contributions to the EDF Coulomb Direct EC H = (1/) d rd r ρ p( r) r r 1 ρ p( r ) Exchange: EC ex = (3/)(3/π) 1/3 d rρ p( r) /3 Spin-Orbit Free parameters ˆv so ij = iw LS ( σ i + σ j) [ k δ( r i r j) k] W LS and r 0L, r 0U Pairing Correlations (E. Garrido et al. Phys. Rev. C 0, 031 (1999)) Zero-range interaction, [ ( ) α ] v pp (ρ( r)) = η v0 ρ( r) 1 γ, ρ 0 = ρ 0 3π k3 F. η multiplicative parameter setting the pairing strength...