Microscopic description of fission using dynamical theories. - PowerPoint PPT Presentation

Microscopic description of fission using dynamical theories. Guillaume SCAMPS Tohoku University Collaboration : C. Simenel, D. Lacroix, K. Hagino, Y. Tanimura Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 1 / 21

Lack of theoretical prediction Lack of theoretical prediction Lots of theoretical questions Error of order of magnitudes on How to define the scission ? the life-time What are the important degrees of Lack of prediction for the freedom ? charge/mass distribution Shell effects ? Effect of pairing ? Odd-even effects ? Prediction are necessary for : How the energy is split into the Astrophysics (r-process) fragments ? Industrial applications, ... production of ions, reactors... 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 Q30 Adibatic path Exact path Q20 Scission 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 264 Fm 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 264 Fm 264 Fm g.s. 280 0 0.5 1 1.5 E g.s. V B t (zs) Pairing energy (MeV) 0 270 E *a dia b Energy (MeV) 132 Sn+ 132 Sn E 0 -0.5 260 Protons Ne utrons -1 250 Protons (a ) Neutrons (b) 240 0 Single particle energy (MeV) -2 230 -4 7 8 9 10 11 12 13 14 15 -6 R (fm) -8 Adiabatic TDHF -10 -12 (c) (d) -14 9 10 11 12 13 14 15 10 11 12 13 14 15 R (fm) R (fm) 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 264 Fm E * = 22 MeV 300 TDHF E 0 263 MeV Energy (MeV) 241 MeV E kin 200 E Coul TKE E kin +E Coul 100 Scission 0 0 0.5 1 1.5 2 t (zs) 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 TDHFB Pairing correlation Independent particle Initialisation : ˆ Quasi-particles : | ω α � = � U α � h MF | φ i � = ǫ i | φ i � V α Evolution : Evolution : i � d | ω α � ∆ i � d ρ = � h � | ω α � dt = [ h MF , ρ ] − ∆ ∗ − h ∗ dt TDHF+BCS Based on TDHFB with the approximation : ∆ ij = δ ij ∆ i dt = (ˆ Evolution : i � d φ i h MF − ǫ i ) φ i i � dn i dt = ∆ ∗ i κ i − ∆ i κ ∗ i i � d κ i dt = κ i ( ǫ i − ǫ i ) + ∆ i (2 n i − 1) Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 8 / 21

Why does we need pairing ? TDHF Fission barrier : 258 Fm -1900 E [MeV] -1920 TDHF+BCS -1940 0 100 200 300 Q 20 [b] 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 ? TDHF Fission barrier : 258 Fm -1900 E [MeV] -1920 TDHF+BCS -1940 0 100 200 300 Q 20 [b] 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 ? TDHF Fission barrier : 258 Fm -1900 E [MeV] -1920 TDHF+BCS -1940 0 100 200 300 Q 20 [b] 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 1.0 350 0.8 300 250 0.6 200 E n i 150 0.4 100 0.2 50 0 0.0 0 10 20 30 40 50 60 -15 -10 -5 0 5 t [10 − 22 s] ǫ i Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 10 / 21

Influence of pairing on fission process 1.0 350 0.8 300 250 0.6 200 E n i 150 0.4 100 0.2 50 0 0.0 0 10 20 30 40 50 60 -15 -10 -5 0 5 t [10 − 22 s] ǫ i Guillaume SCAMPS Microscopic description of fission using dynamical theories. June 23, 2015 10 / 21

258 Fm : 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

258 Fm : Bimodal or trimodal fission ? 3 possible modes Constraint HF+BCS calculations (Skm*) Symmetric compact fragment Energy (MeV) 10 258 Fm Asymmetric elongated fragment 0 sCF sEF -10 aEF 0 100 200 300 Quadrupole moment Q 20 (b) Symmetric elongated fragment 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

258 Fm : TDHF+BCS results Sly4d 3 possible modes -1890 Symmetric compact fragment -1900 V] -1910 E [Me -1920 -1930 -1940 -1950 Asymmetric elongated 0 50 100 150 200 250 300 350 400 450 500 fragment Q 20 [b] 160 140 nts 120 ve 100 Fission e 80 Symmetric elongated fragment 60 40 20 0 140 160 180 200 220 240 260 TKE [Me V] 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

258 Fm : TDHF+BCS results Sly4d 3 possible modes -1890 Symmetric compact fragment -1900 V] -1910 E [Me -1920 -1930 -1940 -1950 Asymmetric elongated 0 50 100 150 200 250 300 350 400 450 500 fragment Q 20 [b] 160 140 nts 120 ve 100 Fission e 80 Symmetric elongated fragment 60 40 20 0 140 160 180 200 220 240 260 TKE [Me V] 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

258 Fm : TDHF+BCS results Sly4d 3 possible modes -1890 Symmetric compact fragment -1900 V] -1910 E [Me -1920 -1930 -1940 -1950 Asymmetric elongated 0 50 100 150 200 250 300 350 400 450 500 fragment Q 20 [b] 160 140 nts 120 ve 100 Fission e 80 Symmetric elongated fragment 60 40 scf 20 0 140 160 180 200 220 240 260 TKE [Me V] 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

258 Fm : TDHF+BCS results Sly4d 3 possible modes -1890 Symmetric compact fragment -1900 V] -1910 E [Me -1920 -1930 -1940 -1950 Asymmetric elongated 0 50 100 150 200 250 300 350 400 450 500 fragment Q 20 [b] 160 140 nts 120 ve 100 Fission e 80 Symmetric elongated fragment 60 40 scf 20 0 140 160 180 200 220 240 260 TKE [Me V] 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

258 Fm : TDHF+BCS results Sly4d 3 possible modes -1890 Symmetric compact fragment -1900 V] -1910 E [Me -1920 -1930 -1940 -1950 Asymmetric elongated 0 50 100 150 200 250 300 350 400 450 500 fragment Q 20 [b] 160 140 nts 120 ve 100 Fission e 80 Symmetric elongated fragment 60 40 aef scf 20 0 140 160 180 200 220 240 260 TKE [Me V] 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

258 Fm : TDHF+BCS results Sly4d 3 possible modes -1890 Symmetric compact fragment -1900 V] -1910 E [Me -1920 -1930 -1940 -1950 Asymmetric elongated 0 50 100 150 200 250 300 350 400 450 500 fragment Q 20 [b] 160 140 nts 120 ve 100 Fission e 80 Symmetric elongated fragment 60 40 aef scf 20 0 140 160 180 200 220 240 260 TKE [Me V] 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