Role of Fission in R-Process Nucleosynthesis

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

94 92 fission 90

88 Solar r abundances 86 84 188 190 186 82

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 ,

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 Protonnumber 2 184 120 TF 18 FRDM 126 110 14

100 10 (MeV) n 2 6 174 S 90 Protonnumber 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

Protonnumber 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 [Möller 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. 10-4 10-5 -6 232 238 10 I Same Th/ U ratio: progenitors of actinides 10-7 solar BCPM have Z < 84 ⇒ can initial nuclei with Z ≥ 84 10-8 FRDM+ TF survive to fission? 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

Averaged ﬁssion rates

1 10 BCPM 2 FRDM+TF 10 0 10 n-induced fission spontan. fission −1 0 10 β-delayed fission 10

−2 ) 10 −2 −1 10

−3 10 Rate(s −4 10 −4 neutron-to-seedratio 10

−6 −5 10 10 n/s

−6 10 −1 0 1 2 3 4 10 10 10 10 10 10 Time (s)

I n-induced dominates until freeze-out and revived by β-delayed neutrons ⇒ β-delayed ﬁssion rates from BCPM barriers required! I decay of material to stability triggers spontaneous ﬁssion. Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

Emitted radioactive energy Energy emitted by radioactive products in NSM crucial for predicting kilonova light curves [J. Barnes et al., ApJ 829 110 (2016)].

100

10-1

BCPM

Fraction of radioactive energy FRDM+TF β-decay α-decay total fission 10-2 10-5 10-4 10-3 10-2 10-1 100 101 102 Days

I Minor impact in the radioactive energy production ⇒ progenitors of actinides from Z < 84 [Mendoza-Temis et al., Phys. Rev. C92, 055805 (2015)]. I Fission subdominant → impact of multi-chance bdf [Mumpower et al., arXiv:1802.04398]? 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

Impact of ﬁssion yields on r process The Astrophysical Journal, 808:30 13pp , 2015 July 20 Eichler et al.

M. Eichler et al., Astrophys. J. 808, 30 (2015). Figure 1. Final abundances of the integrated ejecta around the second and third peak for an NSM Korobkin et al. 2012; Rosswog et al. 2013 at a simulation time 10 s, employing the FRDM mass model combined with four different ssion fragment distribution models see the text . For reasons of clarity the results are presented in two graphs. The abundances for Th and U• areFinal indicated abundances by crosses. In the left-handstrongly panel affected the lower crosses by belongfragments to the Panov distributions et al. 2008 model dashed line , while the lower crosses in the right-hand panel belong to the ABLA07 distribution model dashed line . The dots represent the solar -process abundance pattern Sneden et al. 2008 [see alsoB.C ôté et al., Astrophys. J. 855, 99 (2018)]. • Most of the models are parametrizations/phenomenological → validity far from stability? • This talk: compute fission yields (FY) using DFT+Langevin.

Figure 2. Fission rates at 1 s in s for -delayed and neutron-induced ssion at freeze-out from equilibrium for one representative trajectory when utilizing the FRDM mass model and Panov et al. 2010 ssion rates. : Corresponding ssion fragment production. The distribution model here is ABLA07. Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

The ﬁssion process

J. Sadhukan et al. Phys. Rev. C 93, 011304(R) (2016) Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

The ﬁssion process

J. Sadhukan et al. Phys. Rev. C 93, 011304(R) (2016) Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

The stochastic Langevin framework

Path from outer turning point to scission given by dissipative Langevin:

dpi pj pk ∂ −1 ∂V −1 = − (M )jk − − ηij (M )jk pk + gij Γj (t) dt 2 ∂xi ∂xi |{z} | {z } dx friction random force i = (M−1) p dt ij j

J. Sadhukan et al. Phys. Rev. C 96, 061301(R) (2017) 20

60 11 10 9 (b) 8 30 40 7 6 Q

5 2 20 4 3 1 220 270 320 370 Q20(b) Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

240Pu: Fission yields RAPID COMMUNICATIONS

SADHUKHAN, NAZAREWICZ, AND SCHUNCK PHYSICAL REVIEW C 93, 011304(R) (2016)

J. Sadhukan et al. Phys. Rev. C 96, 061301(R) (2017) in the range of 0 12 30 and ( 11,η22 [30 400 240 Pu with the constraint 1 11/η22 25. Note that we consider 10 10 a very broad range of variations in order to account for the uncertainties in the theoretical determination the dissipation tensor. Finally, the linear pattern in Fig. indicates the 1 1 uncertainty related to the deﬁnition of scission conﬁgurations and corresponds to 0 0. It is very encouraging to see that the predicted yield distributions vary relatively mass0.1 yield (%) 0.1

charge yield (%) little, even for nonphysically large values of ij and . We have also found that the distributions are practically indistin- guishable when the level density parameter varies from A/ to A/13. 120 140 160 50 60 Conclusions. In this work, we propose a microscopic fragment mass fragment charge approach rooted in nuclear DFT to calculate mass and charge FIG. 5. Mass (left) and charge (right) distributions of heavier SF distributions of SF yields. The SF penetrabilities, obtained • Good agreementyields of 240 withPu. The experimental symbols are the data same (circles). as in Fig. . The shaded by minimizing the collective action in large multidimensional regions are uncertainties in the distributions due to variations in PESs with realistic collective inertia, are used as inputs to • Results are(narrow robust red band),against dissipation variations tensor (wider in theoretical cyan band), quantitiesand scission (ηsolveij , E0 the,. . time-dependent . ). dissipative Langevin equations. By • Random forceconfiguration responsible (linear hatch for pattern). the tails of the distribution. combining many trajectories connecting the hypersurface of outer turning points with the scission hypersurface, we predict SF yield distributions. The results of our pilot calculations for restrict the dynamical space in the classically allowed region 240Pu are in excellent agreement with experiment and remain to the surface defined by 20,Q30 . In the following, we reasonably stable under large variations of input parameters. calculate the fission paths on this surface for a collection of This is an important outcome, as SF yield distributions are 900 outer turning points around the most probable out important observables for benchmarking theoretical models The Langevin propagation is studied in three different of SF [52]. This finding is reminiscent of the analysis of scenarios. In the first variant, the mass and charge distributions Ref. [17] for low-energy neutron- and -induced fission, of fission fragments are computed without invoking dissipation which found that the yield distributions predicted in the and fluctuation by setting ij 0 (thus ij 0). Under such Brownian-motion approach are insensitive to large variations conditions, the Langevin equations resemble the deterministic of dissipation tensor. On the other hand, according to our Newtonian equations of motion with a one-to-one correspon- analysis, the collective inertia tensor impacts both tunneling dence between outer turning points and scission points. By and the Langevin dynamics. computing 900 trajectories to scission, we obtain mass and The results of our study confirm that the PESs is the most charge yield distributions marked by the red dashed line in important ingredient when it comes to the maxima of yield Fig. . The most probable values of the fission yields are distributions. This is consistent with the previous DFT studies consistent with the data but the distribution tails are clearly of most probable SF splits [31 53 56], which indicate that the off. In the second variant, we incorporate a constant collective topology of the PES in the prescission region is the crucial dissipation tensor ij with reasonable values 11 50 22 factor. On the other hand, both dissipative collective dynamics 40 , and 12 , but take a diagonal unit mass tensor and collective inertia are essential when it comes to the shape and obtain the green dashed-dotted line. In this case, fission of the yield distributions. The fact that the predictions are fairly dynamics is dominated by the static features of the PES. robust with respect to the details of dissipative aspects of the However, since the excitation energy is small, dissipation model is most encouraging. effects are weak. As a result, the distribution width is even Acknowledgments. Discussions with A. Baran, J. narrower than in the first variant. It is only by combining a Dobaczewski, J. A. Sheikh, and S. Pal are gratefully acknowl- constant dissipation tensor with the nonperturbative cranking edged. This work was supported by the U.S. Department of inertia that we obtain the solid blue lines, which nicely agree Energy, Office of Science, Office of Nuclear Physics under with experiment over the whole range of mass-charge splits. Awards No. DOE-DE-NA0002574 (the Stewardship Science The results shown in Fig. correspond to 100 different runs Academic Alliances program) and No. DE-SC0008511 (NU- per each outer turning point, hence the distributions contain CLEI SciDAC-3 collaboration). Part of this research was per- contribution from 90 000 trajectories. formed under the auspices of the U.S. Department of Energy To illustrate the sensitivity of yield distributions to the by Lawrence Livermore National Laboratory under Contract initial collective energy , the narrow red band in Fig. No. DE-AC52-07NA27344. Computational resources were shows the distribution uncertainty when taking a sample of 11 provided through an INCITE award, “Computational Nuclear different values of within the range 0 2 MeV. Structure,” by the National Center for Computational Sciences While such a variation in changes the SF half-life by (NCCS) and by the National Institute for Computational over two orders of magnitude, its impact on fission yield Sciences (NICS). Computing resources were also provided distributions is minimal. The wider cyan band shows the spread through an award by the Livermore Computing Resource in predicted distributions when sampling the dissipation tensor Center at Lawrence Livermore National Laboratory.

011304-4 Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

Fission yields of 294Og

How robust is the method against:

• Choice of collective variables? • Choice of collective inertias? • Choice of functional?

294 Testground: 118Og176 [Oganessian et al., PRC 74 (2006)] • Heaviest element produced on Earth (2005-2010 JINR, Dubna). • τ ∼ 0.7 ms. • Very few events (1-2 ﬁssion?).

Very exotic nucleus → “blind” EDF calculation. . . 294 208 86 • From localization functions: 118Og176 −−→ 82Pb126 + 36Kr50 . • 294Og decays via cluster emission.

Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

294Og: potential energy surface

• Two competing ﬁssion modes: symmetric( Q30 = 0) vs asymmetric( Q30 6= 0). • 294Og decays via cluster emission.

Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

294Og: potential energy surface

• Two competing ﬁssion modes: symmetric( Q30 = 0) vs asymmetric( Q30 6= 0). 294 208 86 • From localization functions: 118Og176 −−→ 82Pb126 + 36Kr50 . Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

294Og: potential energy surface

• Two competing ﬁssion modes: symmetric( Q30 = 0) vs asymmetric( Q30 6= 0). 294 208 86 • From localization functions: 118Og176 −−→ 82Pb126 + 36Kr50 . • 294Og decays via cluster emission. Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

294Og barriers: UNEDF1 vs D1S

40 UNEDF1HFB 9 ) 3 2 30 r (b ste lu (MeV) Energy 30 20 c fi Q ss 6 10 ion

40 D1S 3

) r 3 2 te 30 lus

(b c

30 20 fis Q s 0 10 ion

0 50 100 150 Q20 (b)

Matheson et al. (in preparation)

UNEDF1 and D1S predict similar evolution of the potential energy surface, but D1S has larger barrier → impact on yields? Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

294Og ﬁssion yields: UNEDF1 vs D1S

1 1

11 11

1 1

11 11

1 1

Matheson et al. (in preparation) 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

Conclusions & Outlook

I HFB + Hauser-Feshbach are valuable tools for studying the role of fission in the r-process nucleosynthesis. I New set of stellar rates suited for r-process calculations: I Abundances sensitive to height of fission barriers and local changes in neutron separation energies around A = 257 and A > 280. I No impact on radioactive energy generation and 232Th/238U ratio: progenitors of actinides have Z < 84 ⇒ no nuclei with Z ≥ 84 survive to fission? I EDF + Langevin is a useful method to compute fission yields → small sensitivity on choice of the functional.

I Future work: - β-delayed fission rates from BCPM barriers; - calculation of fission fragments distributions using EDFs; - explore different initial astrophysical conditions; - extend calculations using different EDF. Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

Some questions

• Which observables could prove the production of actinides/SHE during the r process? (see Y. Zhu et al., arXiv:1806.09724 and Nicole’s talk)

• How shall we conciliate consistency and accuracy in the calculations of nuclear inputs? (Nicolas’ talk)

• Is it time for new sensitivity studies of r-process abundances? (see L. Neufcourt et al., arXiv:1806.00552 Witek’s talk) Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

Collaborators

- G. Mart´ınez Pinedo (TUD/GSI, Darmstadt) - Z. Matheson and W. Nazarewicz (NSCL/FRIB, East Lansing) - L. Robledo (UAM, Madrid) - J. Sadhukhan (VECC, Kulkata) - N. Schunck (LLNL, Livermore) - M.-R. Wu (Sinica, Taiwai)

Thank you! The dynamic description of spontaneous ﬁssion

Z b q tSF ∼ exp(2S) ⇐ S(L) = ds 2 × B(s) E(s) − E0 a

Expand the multidimensional PES: relevant d.o.f. in s?

I Deformation multipoles: Q20, Q22, Q30,... I Pairing correlations ∆ (Babinet and Moretto, PLB 49 (1974)).

How to determine the ﬁssion path L(s)? I Minimizing the energy E(s): static approximation. I Minimizing the action S(L): dynamic approach.

State-of-the-art SF calculations: Sadhukhan et al, PRC88(2013) and PRC90(2014); SAG et al, PRC90(2014); Zhao et al, PRC92(2015) and PRC93(2016). Pairing ﬂuctuations restore the axial symmetry! Artifact?

Static vs dynamic ﬁssion: 240Pu and 234U

Triaxial case: 240Pu - SkM* interaction

E(s) [MeV]

from Shadukhan et al., PRC90(2014), see also Zhao et al., PRC93(2016).

[b] dynamic paths: 22

Q 2D: s = {Q20, Q22} 2 3D: s = {Q20, Q22, ∆N }

Q20 [b] Pairing ﬂuctuations restore the axial symmetry! Artifact?

Static vs dynamic ﬁssion: 240Pu and 234U

Triaxial case: 240Pu - SkM* interaction

E(s) [MeV]

from Shadukhan et al., PRC90(2014), see also Zhao et al., PRC93(2016).

dynamic paths: [b]

22 2D: s = {Q20, Q22}

Q 2 3D: s = {Q20, Q22, ∆N }

Q20 [b] Static vs dynamic ﬁssion: 240Pu and 234U

Triaxial case: 240Pu - SkM* interaction

E(s) [MeV]

from Shadukhan et al., PRC90(2014), see also Zhao et al., PRC93(2016).

dynamic paths: [b]

22 2D: s = {Q20, Q22}

Q 2 3D: s = {Q20, Q22, ∆N }

Q20 [b]

Pairing ﬂuctuations restore the axial symmetry! Artifact? Conclusion

Spontaneous fission dynamics strongly modified by pairing fluctuations!

Static vs dynamic ﬁssion: 240Pu and 234U Axial case: 234U - BCPM interaction

Method tsf (s) 43 Emin (static) 0.81 × 10 42 Smin(Q20, Q30) 0.44 × 10 43 Smin(Q20, Q40) 0.12 × 10 2 23 Smin(Q20, ∆N ) 0.18 × 10 Experiment 7.8 × 1023

SAG, Robledo and Guzm´an-Rodriguez PRC90(2014).

- Pairing correlations reduce collective inertias → spontaneous ﬁssion lifetimes decrease when pairing is included as d.o.f. Static vs dynamic ﬁssion: 240Pu and 234U Axial case: 234U - BCPM interaction

Method tsf (s) 43 Emin (static) 0.81 × 10 42 Smin(Q20, Q30) 0.44 × 10 43 Smin(Q20, Q40) 0.12 × 10 2 23 Smin(Q20, ∆N ) 0.18 × 10 Experiment 7.8 × 1023

SAG, Robledo and Guzm´an-Rodriguez PRC90(2014).

- Pairing correlations reduce collective inertias → spontaneous ﬁssion lifetimes decrease when pairing is included as d.o.f.

Conclusion

Spontaneous fission dynamics strongly modified by pairing fluctuations!