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

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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

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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

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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

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

The r process

r(apid neutron capture) process: τn ≪ τβ−

β decay neutron capture neutron shell closure

N

Z

unstable nuclei stable nuclei

How far can the r process proceed? Number of free neutrons that seed nuclei can capture (neutron-to-seed ratio).

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

r process and fission

100 150 200 250 10

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r−process waiting point (ETFSI−Q) Known mass Known half−life N=126 N=82

Solar r abundances

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N=184

30 32 28

f i s s i

n

For large neutron-to-seed ratio fission is unavoidable

n-induced fission
β-delayed fission
spontaneous fission

◮ Where does fission occur? ◮ How much material accumulates in fissioning region? ◮ What are the fission yields?

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

1) Compute fission properties and binding energies using BCPM EDF.

120 140 160 180 200 220 240 Neutron number 90 100 110 120 Proton number

Sn = 2 MeV Sn = 0 MeV

2

2 4 6 8 10 12 14

Bf−Sn (MeV)

2) Calculate stellar reaction rates from Hauser-Feshbach theory.

120 140 160 180 200 220 240 Neutron number 90 100 110 120 Proton number

Dominating channel at nn =1028 cm−3

(n,γ) (n,fission)

spont. fission

Sn= 2 MeV Sn= 0 MeV

3) Obtain r-process abundances using network calculations.

120 140 160 180 200 220 240 Neutron number 90 100 110 120 Proton number

25
20
15
10
5

log10(Y)

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

The fission process

10 20 30 40 50 60 70 80 Q20 (b)

2050
2045
2040
2035

EHFB (MeV) 286Fl 114 inner barrier fission isomer

uter

barrier ground state

E*

spontaneous fission neutron-induced beta-delayed photo-induced fission

Potential Energy Surface Energy evolution from the initial state to the scission point.

SAG+ PRC90(2014); Sadhukhan+ PRC90(2014)

Collective inertias Resistance

f

the nucleus against the deformation forces.

Baran+ PRC84 (2011)

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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[|Ψ] = 0 , where |Ψ is a quasiparticle (β) vacuum: |Ψ =

µ

βµ|0 ⇒ βµ|Ψ = 0 . 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 − λq 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.

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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

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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.

2 4 6 8 10 12 14

Fission barrier (MeV)

120 140 160 180 200 220 240 Neutron number 90 100 110 120 Proton number TF 90 100 110 120 Proton number BCPM

Sn = 2 MeV Sn = 0 MeV

2 6 10 14 18 S2n (MeV)

184 126 174 BCPM

90 100 110 120 Proton number 2 6 10 14 18 S2n (MeV)

184 126 174 FRDM

BCPM: Giuliani et al. (2018); TF: Myers and ´ Swiat ¸ecky (1999); FRDM: M¨

ller et al. (1995).

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

Compound reactions

Reaction rates computed within the Hauser-Feshbach statistical model.

compound nucleus target

γ

gamma decay particle emission 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.

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

Cross sections from BCPM

Energy (MeV) 101 102 103 104 σ(n,fiss) (mb) 235U(n,fis) Experiment BCPM Energy (MeV) 238U(n,fis) Energy (MeV) 238Pu(n,fis) 10-2 10-1 100 101 Energy (MeV) 101 102 103 104 σ(n,γ) (mb) 235U(n,g) 10-2 10-1 100 101 Energy (MeV) 238U(n,g) 10-2 10-1 100 101 Energy (MeV) 238Pu(n,g)

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

Stellar reaction rates - impact of collective inertias?

120 140 160 180 200 220 240 Neutron number 90 100 110 120 SEMP-r 90 100 110 120 Proton number GCM-r

Sn = 2 MeV Sn = 0 MeV

90 100 110 120 ATDHFB-r

spont. fis.

α-decay (n,γ) (n,α) (n,fis) (n,2n) SAG, Mart´ ınez-Pinedo and Robledo, Phys. Rev. C 97, 034323 (2018)

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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.

x [km] y [km] 30 20 10 10 20 30 30 20 10 10 20 30 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 x [km] y [km] 30 20 10 10 20 30 30 20 10 10 20 30 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 13.0056 ms 13.4824 ms x [km] y [km] 13.8024 ms 50 50 50 40 30 20 10 10 20 30 40 50 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 x [km] y [km] 15.167 ms 50 50 50 40 30 20 10 10 20 30 40 50 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5

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?

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

r-process abundances: BCPM vs FRDM+TF

◮ Trajectory: 3D relativistic simulations from 1.35 M⊙-1.35 M⊙ NS mergers [Bauswein+(2013)]. ◮ BCPM Giuliani+(2017) vs TF+FRDM Panov+(2010). ◮ We changed the rates of nuclei with Z ≥ 84. ◮ Same β-decay rates [M¨

ller et al. PRC67(2003)].

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abundances at n/s=1

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abundances at τ(n,γ) = τβ

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abundances at 1 Gyr solar BCPM FRDM+ TF

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

r-process abundances: BCPM vs FRDM+TF

◮ Trajectory: 3D relativistic simulations from 1.35 M⊙-1.35 M⊙ NS mergers [Bauswein+(2013)]. ◮ BCPM Giuliani+(2017) vs TF+FRDM Panov+(2010). ◮ We changed the rates of nuclei with Z ≥ 84. ◮ Same β-decay rates [M¨

ller et al. PRC67(2003)].

◮ BCPM barriers larger than TF:

nuclei around A > 280 longer lifetimes ,
accumulation above 2nd peak.

◮ BCPM shell gap smaller than FRDM at N = 174:

FRDM-TF peak at A ∼ 257,
impact on final abundances at A ∼ 110.

◮ Same 232Th/238U ratio: progenitors of actinides have Z < 84 ⇒ can initial nuclei with Z ≥ 84 survive to fission?

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abundances at 1 Gyr solar BCPM FRDM+ TF

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

r-process abundances: BCPM vs FRDM+TF

◮ Trajectory: 3D relativistic simulations from 1.35 M⊙-1.35 M⊙ NS mergers [Bauswein+(2013)]. ◮ BCPM Giuliani+(2017) vs TF+FRDM Panov+(2010). ◮ We changed the rates of nuclei with Z ≥ 84. ◮ Same β-decay rates [M¨

ller et al. PRC67(2003)].

◮ BCPM barriers larger than TF:

nuclei around A > 280 longer lifetimes ,
accumulation above 2nd peak.

◮ BCPM shell gap smaller than FRDM at N = 174:

FRDM-TF peak at A ∼ 257,
impact on final abundances at A ∼ 110.

◮ Same 232Th/238U ratio: progenitors of actinides have Z < 84 ⇒ can initial nuclei with Z ≥ 84 survive to fission?

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abundances at 1 Gyr solar BCPM FRDM+ TF

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

r-process abundances: BCPM vs FRDM+TF

◮ Trajectory: 3D relativistic simulations from 1.35 M⊙-1.35 M⊙ NS mergers [Bauswein+(2013)]. ◮ BCPM Giuliani+(2017) vs TF+FRDM Panov+(2010). ◮ We changed the rates of nuclei with Z ≥ 84. ◮ Same β-decay rates [M¨

ller et al. PRC67(2003)].

◮ BCPM barriers larger than TF:

nuclei around A > 280 longer lifetimes ,
accumulation above 2nd peak.

◮ BCPM shell gap smaller than FRDM at N = 174:

FRDM-TF peak at A ∼ 257,
impact on final abundances at A ∼ 110.

◮ Same 232Th/238U ratio: progenitors of actinides have Z < 84 ⇒ can initial nuclei with Z ≥ 84 survive to fission?

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abundances at n/s=1

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abundances at τ(n,γ) = τβ

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abundances at 1 Gyr solar BCPM FRDM+ TF

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

Averaged fission rates

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Time (s) 10

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Rate (s−1) BCPM FRDM+TF n-induced fission

spontan. fission

β-delayed fission 10

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neutron-to-seed ratio n/s

◮ n-induced dominates until freeze-out and revived by β-delayed neutrons ⇒ β-delayed fission rates from BCPM barriers required! ◮ decay of material to stability triggers spontaneous fission.

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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)].

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

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

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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

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

Impact of fission yields on r process

M. Eichler et al., Astrophys. J. 808, 30 (2015).
Final abundances strongly affected by fragments distributions

[see also B. Cˆ

t´

e 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.

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

The fission process

J. Sadhukan et al. Phys. Rev. C 93, 011304(R) (2016)

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

The fission process

J. Sadhukan et al. Phys. Rev. C 93, 011304(R) (2016)

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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 dt = −pjpk 2 ∂ ∂xi (M−1)jk − ∂V ∂xi − ηij

friction

(M−1)jkpk + gijΓj(t)

random force

dxi dt = (M−1)ijpj

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

20 220 270 320 370 20 40 60

11 10 9 8 7 6 5 4 3 2 1

Q20(b) Q30(b)

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

240Pu: Fission yields

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

50 60 0.1 1 10 120 140 160 0.1 1 10

240Pu

charge yield (%) fragment charge mass yield (%) fragment mass

Good agreement with experimental data (circles).
Results are robust against variations in theoretical quantities (ηij, E0,. . . ).
Random force responsible for the tails of the distribution.

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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?

Testground: 294

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. . .

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

294Og: potential energy surface

Two competing fission modes: symmetric (Q30 = 0) vs asymmetric (Q30 = 0).

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

294Og: potential energy surface

Two competing fission modes: symmetric (Q30 = 0) vs asymmetric (Q30 = 0).
From localization functions: 294

118Og176 −

− → 208

82Pb126 + 86 36Kr50 .

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

294Og: potential energy surface

Two competing fission modes: symmetric (Q30 = 0) vs asymmetric (Q30 = 0).
From localization functions: 294

118Og176 −

− → 208

82Pb126 + 86 36Kr50 .

294Og decays via cluster emission.

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

294Og barriers: UNEDF1 vs D1S 10 20 30 40 Q30 (b

3 2)

UNEDF1H F B 50 100 150 Q20 (b) 10 20 30 40 Q30 (b

3 2)

D1S 3 6 9 Energy (MeV) cluster fission cluster fission

Matheson et al. (in preparation)

UNEDF1 and D1S predict similar evolution of the potential energy surface, but D1S has larger barrier → impact on yields?

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

294Og fission yields: UNEDF1 vs D1S

160 180 200 220 Heavy fragment mass 10−1 100 101 % yield UNEDF1HFB D1S 60 70 80 90 Heavy fragment charge 10−1 100 101

294Og Matheson et al. (in preparation)

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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

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Introduction Fission and r process Fission fragments distributions Conclusions & Outlook

Conclusions & Outlook

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

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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)

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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!

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The dynamic description of spontaneous fission

tSF ∼ exp(2S) ⇐ S(L) =

b

a

ds

2 × B(s)

E(s) − E0

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

◮ Deformation multipoles: Q20, Q22, Q30, . . . ◮ Pairing correlations ∆ (Babinet and Moretto, PLB 49 (1974)). How to determine the fission path L(s)? ◮ Minimizing the energy E(s): static approximation. ◮ 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).

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Static vs dynamic fission: 240Pu and 234U

Triaxial case: 240Pu - SkM* interaction

Q20 [b]

Q22 [b]

E(s) [MeV]

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

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

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Static vs dynamic fission: 240Pu and 234U

Triaxial case: 240Pu - SkM* interaction

Q20 [b]

Q22 [b]

E(s) [MeV]

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

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

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Static vs dynamic fission: 240Pu and 234U

Triaxial case: 240Pu - SkM* interaction

Q20 [b]

Q22 [b]

E(s) [MeV]

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

dynamic paths: 2D: s = {Q20, Q22} 3D: s = {Q20, Q22, ∆N 2} Pairing fluctuations restore the axial symmetry! Artifact?

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Static vs dynamic fission: 240Pu and 234U

Axial case: 234U - BCPM interaction Method tsf (s) Emin (static) 0.81 × 1043 Smin(Q20, Q30) 0.44 × 1042 Smin(Q20, Q40) 0.12 × 1043 Smin(Q20, ∆N 2) 0.18 × 1023 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.

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Static vs dynamic fission: 240Pu and 234U

Axial case: 234U - BCPM interaction Method tsf (s) Emin (static) 0.81 × 1043 Smin(Q20, Q30) 0.44 × 1042 Smin(Q20, Q40) 0.12 × 1043 Smin(Q20, ∆N 2) 0.18 × 1023 Experiment 7.8 × 1023

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

Pairing correlations reduce collective inertias → spontaneous fission