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Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 1 / 21

Microscopic description of fission using dynamical theories.

Guillaume SCAMPS

Tohoku University Collaboration : C. Simenel, D. Lacroix,

• K. Hagino, Y. Tanimura

Lack of theoretical prediction

Lack of theoretical prediction

Error of order of magnitudes on the life-time Lack of prediction for the charge/mass distribution

Prediction are necessary for :

Astrophysics (r-process) Industrial applications, production of ions, reactors...

Lots of theoretical questions

How to define the scission ? What are the important degrees of freedom ? Shell effects ? Effect of pairing ? Odd-even effects ? How the energy is split into the fragments ? ...

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 2 / 21

State of the art :

Macroscopical model Liquid drop Static with shell correction

• P. Moller, et al., Nature 409 (2001)

Dynamics Stochastic motion

• J. Randrup, PRL 106 (2011)

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 3 / 21

State of the art :

Macroscopical model Microscopical model Liquid drop Mean-field theory with pairing, Static with shell correction HF+BCS or HFB

• P. Moller, et al., Nature 409 (2001)
• A. Staszczak, et al., PRC 80, (2009)

Dynamics Stochastic motion Dynamical mean-field TDHF+BCS

• J. Randrup, PRL 106 (2011)
• G. Scamps, et al, arXiv :1501.03592

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 3 / 21

Adiabatic approximation

Q20 Q30 Scission Adibatic path Exact path

Adiabatic path

Path that minimize the energy with respect to degrees of freedom orthogonal to the elongation.

TDHF or TDHF+BCS

All the degrees of freedom are taken into account

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 4 / 21

TDHF calculation, fission of 264Fm

Adiabatique Non adiabatique

• C. Simenel and A. S. Umar, Phys. Rev. C 89, 031601(R), 2014

The adiabaticity approximation is assumed for the barrier crossing but is known to break down before scission.

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 5 / 21

TDHF calculation, fission of 264Fm

t (zs)

0.5 1 1.5 7 8 9 10 11 12 13 14 15

R (fm)

230 240 250 260 270 280

Energy (MeV)

264Fm g.s.

VB E0

132Sn+ 132Sn

Eg.s. E*a

dia b

Adiabatic TDHF

• 1
• 0.5

Pairing energy (MeV)

9 10 11 12 13 14 15

R (fm)

• 14
• 12
• 10
• 8
• 6
• 4
• 2

Single particle energy (MeV) Protons

10 11 12 13 14 15

R (fm) Neutrons

Protons Ne utrons

(a ) (b) (c) (d)

• C. Simenel and A. S. Umar, Phys. Rev. C 89, 031601(R), 2014

The adiabaticity is not assume in the TDHF evolution

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 6 / 21

TDHF calculation, fission of 264Fm

0.5 1 1.5 2

t (zs)

100 200 300

Energy (MeV) Ekin ECoul Ekin+ECoul E *

TDHF

E0 TKE Scission = 22 MeV

241 MeV 263 MeV

• C. Simenel and A. S. Umar, Phys. Rev. C 89, 031601(R), 2014

Conclusion

Total Kinetic energy = 241 MeV Excitation energy = E∗

adiabatic + E∗ TDHF = 34 MeV

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 7 / 21

Mean-field theory with pairing

TDHF

Independent particle Initialisation : ˆ hMF |φi = ǫi |φi Evolution : i dρ

dt = [hMF, ρ]

TDHFB

Pairing correlation Quasi-particles : |ωα = Uα

Vα

• Evolution :

i d|ωα

dt

=

h ∆ −∆∗ −h∗

• |ωα

TDHF+BCS

Based on TDHFB with the approximation : ∆ij = δij∆i Evolution : i dφi

dt = (ˆ

hMF − ǫi)φi i dni

dt = ∆∗ i κi − ∆iκ∗ i

i dκi

dt = κi(ǫi − ǫi) + ∆i(2ni − 1)

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 8 / 21

Why does we need pairing ?

Fission barrier : 258Fm

• 1940
• 1920
• 1900

E[MeV]

100 200 300

Q20[b]

TDHF TDHF+BCS

• G. Scamps, C. Simenel, D. Lacroix, arXiv :1501.03592 [nucl-th]

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 9 / 21

Why does we need pairing ?

Fission barrier : 258Fm

• 1940
• 1920
• 1900

E[MeV]

100 200 300

Q20[b]

TDHF TDHF+BCS

• G. Scamps, C. Simenel, D. Lacroix, arXiv :1501.03592 [nucl-th]

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 9 / 21

Why does we need pairing ?

Fission barrier : 258Fm

• 1940
• 1920
• 1900

E[MeV]

100 200 300

Q20[b]

TDHF TDHF+BCS

• G. Scamps, C. Simenel, D. Lacroix, arXiv :1501.03592 [nucl-th]

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 9 / 21

Influence of pairing on fission process

50 100 150 200 250 300 350 10 20 30 40 50 60 0.0 0.2 0.4 0.6 0.8 1.0

• 15
• 10
• 5

5 E t[10−22 s] ni ǫi

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 10 / 21

Influence of pairing on fission process

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 10 / 21

50 100 150 200 250 300 350 10 20 30 40 50 60 0.0 0.2 0.4 0.6 0.8 1.0

• 15
• 10
• 5

5 E t[10−22 s] ni ǫi

258Fm : Experimental results

• E. K. Hulet, J. F. Wild, R. J.

Dougan, R. W. Lougheed,et al., PRC 40, 770 (1989)

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 11 / 21

258Fm : Bimodal or trimodal fission ?

3 possible modes

Symmetric compact fragment Asymmetric elongated fragment Symmetric elongated fragment Constraint HF+BCS calculations (Skm*)

• 10

10 100 200 300 258Fm

Energy (MeV)

sCF sEF aEF

Quadrupole moment Q20 (b)

• A. Staszczak, A. Baran, J. Dobaczewski, and W. Nazarewicz,

PRC 80, 014309 (2009)

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 12 / 21

258Fm : TDHF+BCS results

3 possible modes

Symmetric compact fragment Asymmetric elongated fragment Symmetric elongated fragment

Sly4d

20 40 60 80 100 120 140 160 140 160 180 200 220 240 260

Fission e ve nts TKE [Me V]

• 1950
• 1940
• 1930
• 1920
• 1910
• 1900
• 1890

50 100 150 200 250 300 350 400 450 500

E [Me V] Q20[b]

• G. Scamps, C. Simenel, D. Lacroix, arXiv :1501.03592 [nucl-th]

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 13 / 21

258Fm : TDHF+BCS results

3 possible modes

Symmetric compact fragment Asymmetric elongated fragment Symmetric elongated fragment

Sly4d

20 40 60 80 100 120 140 160 140 160 180 200 220 240 260

Fission e ve nts TKE [Me V]

• 1950
• 1940
• 1930
• 1920
• 1910
• 1900
• 1890

50 100 150 200 250 300 350 400 450 500

E [Me V] Q20[b]

• G. Scamps, C. Simenel, D. Lacroix, arXiv :1501.03592 [nucl-th]

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 13 / 21

258Fm : TDHF+BCS results

3 possible modes

Symmetric compact fragment Asymmetric elongated fragment Symmetric elongated fragment

Sly4d

20 40 60 80 100 120 140 160 140 160 180 200 220 240 260

scf

Fission e ve nts TKE [Me V]

• 1950
• 1940
• 1930
• 1920
• 1910
• 1900
• 1890

50 100 150 200 250 300 350 400 450 500

E [Me V] Q20[b]

• G. Scamps, C. Simenel, D. Lacroix, arXiv :1501.03592 [nucl-th]

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 13 / 21

258Fm : TDHF+BCS results

3 possible modes

Symmetric compact fragment Asymmetric elongated fragment Symmetric elongated fragment

Sly4d

20 40 60 80 100 120 140 160 140 160 180 200 220 240 260

scf

Fission e ve nts TKE [Me V]

• 1950
• 1940
• 1930
• 1920
• 1910
• 1900
• 1890

50 100 150 200 250 300 350 400 450 500

E [Me V] Q20[b]

• G. Scamps, C. Simenel, D. Lacroix, arXiv :1501.03592 [nucl-th]

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 13 / 21

258Fm : TDHF+BCS results

3 possible modes

Symmetric compact fragment Asymmetric elongated fragment Symmetric elongated fragment

Sly4d

20 40 60 80 100 120 140 160 140 160 180 200 220 240 260

aef scf

Fission e ve nts TKE [Me V]

• 1950
• 1940
• 1930
• 1920
• 1910
• 1900
• 1890

50 100 150 200 250 300 350 400 450 500

E [Me V] Q20[b]

• G. Scamps, C. Simenel, D. Lacroix, arXiv :1501.03592 [nucl-th]

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 13 / 21

258Fm : TDHF+BCS results

3 possible modes

Symmetric compact fragment Asymmetric elongated fragment Symmetric elongated fragment

Sly4d

20 40 60 80 100 120 140 160 140 160 180 200 220 240 260

aef scf

Fission e ve nts TKE [Me V]

• 1950
• 1940
• 1930
• 1920
• 1910
• 1900
• 1890

50 100 150 200 250 300 350 400 450 500

E [Me V] Q20[b]

• G. Scamps, C. Simenel, D. Lacroix, arXiv :1501.03592 [nucl-th]

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 13 / 21

258Fm : TDHF+BCS results

3 possible modes

Symmetric compact fragment Asymmetric elongated fragment Symmetric elongated fragment

Sly4d

20 40 60 80 100 120 140 160 140 160 180 200 220 240 260

sef aef scf

Fission e ve nts TKE [Me V]

• 1950
• 1940
• 1930
• 1920
• 1910
• 1900
• 1890

50 100 150 200 250 300 350 400 450 500

E [Me V] Q20[b]

• G. Scamps, C. Simenel, D. Lacroix, arXiv :1501.03592 [nucl-th]

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 13 / 21

Distribution of number of particles

Projection technique

Proba (N part. on the left)= Ψ|ˆ Pleft(N)|Ψ TDHF : C. Simenel, PRL 105 (2010) TDHF+BCS : G. Scamps and D. Lacroix, PRC 87, 014605 (2013)

Results

0.0 0.1 0.2 0.3 72 74 76 78 80 82 84 86

P(N) N

TDHF TDHF+BCS

Conclusion

Reproduction of the odd-even effect with TDHF+BCS

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 14 / 21

Distribution of number of particles

Results

0.0 0.1 0.2 0.3 75 80 85 90 95 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 46 48 50 52 54 56 58 60

a) b) P(N) N P(Z) Z

Experimental data

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 15 / 21

Systematic comparison for actinide

Comparison with experimental data

TDHF+BCS results for 230Th, 234U,

236U, 240Pu, 246Cm, 250Cf

50 52 54 56 58

Zfrag

230 235 240 245 250

A

Experimental data K.-H. Schmidt et al. Nuclear Physics A 665 (2000)

Conclusion

→ Good reproduction of the Z≃54 "magic" number

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 16 / 21

TDHF with Balian-Vénéroni variational principle

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 17 / 21

TDHF with Balian-Vénéroni variational principle

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 17 / 21

TDHF with Balian-Vénéroni variational principle

Results

t (zs)

0.5 1 1.5 7 8 9 10 11 12 13 14 15

R (fm)

230 240 250 260 270 280

Energy (MeV)

264Fm g.s.

VB E0

132Sn+ 132Sn

Eg.s. E*a

dia b

σ2

TDHF = 1.35, σ2 BV = 2.35 10-4 10-3 10-2 10

• 1

1

• 10
• 5

5 10 15

P(A) A-A

TDHF BV exp

Conclusion

BV provides the fluctuations for the scission process Need initial fluctuations (second part of the talk)

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 18 / 21

Conclusion TDHF+BCS

Conclusion

Good reproduction of the total kinetic energy Important effect of pairing on fission process (J. W. Negele, et al. (1978)) Reproduction of the even-odd effects Reproduction of the Z≃54 behavior Fluctuation obtained with Balian-Vénéroni method (for TDHF)

Prospects

Finite temperature calculation Description of the evaporation Study of the collective excitation after the scission

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 19 / 21

Outlooks

Deformation Energy Tunneling Superfluidity Dissipation Non-adiabaticity

Initial potential Barrier

Beyond the WKB approximation Beyond the adiabatic approximation Fluctuations ...

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 20 / 21

Thank you

Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 21 / 21