Nuclear fission: its relation to and impacts on r-process nucleosynthesis and formation/properties of super-heavy elements

Satoshi Chiba (千葉 敏）

原子核でつむぐrプロセス2019.05.22-24京都大学・基礎物理学研究所（パナソニック国際ホール）

Prof., Deputy director, Laboratory for Advanced Nuclear Energy, Institute of Innovative Research, Tokyo Institute of Technology (Tokyo Tech.)

Director, Atomic Energy Society of JapanForeign guest professor, Beihang University, Beijing

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Contents

1. Announcements2. Background3. Research in nuclear fission study by Tokyo Tech.

implementation of 4-D Langevin equation : • correlated transitions in mass and TKE distributions

of fission fragments, and fission in SHE4. Study on formation mechanisms of Z=120 elements

with a hybrid model: • AMD (or Cb-TDHFB) + Langevin + Hauser-

Feshbach theories5. Concluding remarks

International workshop on nuclear physics for astrophysical phenomenaDate: Oct. 23rd-25th, 2019Confirmed invited speakers: Stéphane Goriely(ULB), Gabriel Martínez-Pinedo (IKP)Topics: Nuclear physics relating to astrophysical phenomenaKey topics: Nucleosyntheisis, nuclear EOS, fission, mass table, beta decay etc.Venue: Tokyo Institute of Technology, Tokyo, Japan

Workshop registration and the website will be announced soon (in early July) Contact: chikako@lane.iir.titech.ac.jp

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Theoretical study on nuclear fission

Astrophysical applications

Kajino, Wanajo, Hayakawa, Suzuki, et al.

Nuclear Data Library: JENDL

Parametrization of FPYNeutron cross sectionsNeutrino cross sectionsPhenomenology

Hauser-Feshbach

Fission mechanismsSHE formation

• Langevin model• AMD• TDHFB• HFB• Hauser-Feshbach

theory• Gross Theory of β-

decay

Fission study at Tokyo Tech.

Evaluation of neutron cross sections and fission yield data for nuclear energy

5

Our FPY data was employed in fission recycling calculation

6

Our branching ratio data for neutrino cross sections was employed

7

Background: Nuclear fission and SHE

1. Nuclear fission is the key physics process as a base in nuclear technologies, especially for estimation of reactor kinetics, inventory of radioactive nuclei in spent nuclear fuel, material damage, and so on, so accurate data is necessary

2. Nuclear fission is also important in understanding origin of elements in r-process nucleosynthesis in the cosmos, since fission recycling is believed to occur in binary NS merger scenario, gravitational wave and signature of heavy elements from which have been observed and now are important parts of "multimessenger astronomy“. Here, not only isotope distribution but also kinetic energy of FF is important as a source of local heating

3. Understanding of nuclear fission is essential in the synthesis of superheavy elements (SHE), since fission prevents formation of SHE as a major competing process

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Background: Nuclear fission and SHE

6. Due to complexity of the process as a large-amplitude collective motion, however, nuclear fission still offers a field of big challenges to nuclear physics, especially, the process from formation of excited compound nucleus to scission is still a mysterious process

7. Many observables arise as a result of fission, e.g., fission fragment yield, TKE, population of prompt neutrons and gammas which is followed by a series of β-decay, and their correlations must be comprehended in a consistent manner, which is still a difficult subject

8. We have been treating the process before scission by several theories, such as Langevin equation, Antisymmetrized Molecular Dynamics （AMD) and Time-Dependent Hartree-Fock （TDHF), and their outcomes are to be connected to statistical decay model and theory of β-decay

9. These methodologies can be applied also to study of fission and formation of Super Heavy Element (SHE）, later part of my talk is devoted to this subject

Systematics of average peak position of light (L) and heavy (H) fragments

<AH>～140

<AL>

A=258-260

258Fm

234U

<AH><AL>

Some kind of transition in fission mechanisms is taking place between them

9

10

Itkis et al., Nucl. Phys. A944(2015)204-237

Peak position at broader region of nuclei

AH～140

AL～132

• How these changes in the systematics and anomalies in peak positions can be understood?

• Fission of SHE is important for r-process

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Systematics and anomaly in the average Total Kinetic Energy of Fission Fragments

How can we understand these systematical and anomalous trends simultaneously?

Nuclear fission treated by Langevin equation

These 2 different d.o.f have different time scales:

Brownian motion

• nucleon motion : 1 to 10 fm/c

• shape motion : ～>10,000fm/c

Nuclear shape evolution is driven by random kicks by nucleons in thermal equilibrium (microscopic d.o.f.) given to the nuclear surface (macroscopic d.o.f) inside the surface

12

13

Two-center model(Maruhn and Greiner, Z. Phys. 251(1972) 431)

Shape parametrization

: Radius of compound nucleus

Mass asymmetry

Elongation

Deformation of fragmentsii

iii ba

ba+-

=2

)(3d

●

●

●

RzZZ 0

0 =

21

21

AAAA

+-

=a

R

35.0=e neck parameter : fixed●

● volume conservation condition is applied

Rneck

Collective coordinates （3 or 4 dynamical variables)

{ } },,,{ 2104 addZZq D =

fragmentleft theof mass : fragmentright theof mass :

2

1

AA

3/12.1 CNA=

No free parameter

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4D Langevin model

qi : Nuclear shape motion pi : Momentum conjugate to qiF : Helmholtz' free energy, 𝐹 = 𝑉 − 𝑇𝑆mij : Inertia tensor : Werner-Wheeler model or Linear Response Theory

γij : friction tensor: Wall and Window or Linear Response Theory

( )1ijij

dq m pdt

-=

{qi : 𝑖 = 1. . 4}={𝑍𝑍,, α , δ1, δ2 }

：Fluctuation dissipation theorem (+Einstein relation)

𝐸∗：Total excitation energy of the system

Drift term/01/2

= − 34351

− 673351

𝑚96:;𝑝:𝑝; − 𝛾>: 𝑚96

:;𝑝; + 𝑔>:𝑅: 𝑡

C.Ishizuka et al., PRC 96, 064616 (2017).

Friction term Wiener term

1*2 ij i j rotE m p p E

Ta

- -=

𝑔>:𝑔>: = 𝛾>:𝑇

: 2-center Woods-Saxon model

Nuclear model calculation

i ii

i ii

dV TdS PdV K q

dT K q

= - -

= -

å

å

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Temperature dependent free energy surface F

Shell effects disappears at T>2MeV

ZZ0

F

236U

F.A.Ivanyuk, C.Ishizuka, M.D.Usang and SC, Phys. Rev. C 97, 054331 (2018)

→ Ignatyuk type damping function is not correct below Tcrit

Macro-Micro calculation4D Woods-SaxonStrutinsky shell correctionBCS pair correction

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Example of Langevin trajectories (236U, 20MeV)

V(MeV)

RzZZ 0

0 =

Rneck=0

ElongationMas

s as

ymm

etr

yNot differentiable everywhereInfinite path length when δt→0

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234U 238Np

240Pu242Am

Predictions for mass distributions (Ex=20MeV)

18

Decomposition of fission modes (Brosa)

asymmetric components (Standard 1 & 2 modes)

Symmetric component:Superlong mode

236UStandard 1,2Super Long

Super Short

Q-value

Mass-TKE correlation and its decompositionStandard 1,2

Clear transition of fission mechanisms, symmetric mode begin super long for 236U, while it is super short for 258Fm

258Fm

19

20

Systematics in Mass-TKE correlationsLook carefully how the symmetric component behaves. Look also how the dominant mode (red contour part) changes

21

Systematics in Mass-TKE correlations

22

Results of mass-TKE correlations

(ε=0.35)

Let us look how the symmetric component and dominant mode behave as a function of the Z2/A1/3

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Results of mass-TKE correlations

(ε=0.35)

Let us look how the symmetric component and dominant mode behave as a function of the Z2/A1/3

Systematic measurement of such mass-TKE correlation will be very important to understand fission mechanisms, especially in the transition region

We can understand the systematical and anomalous trends in mass and TKE distributions of these nuclei in terms of correlated transition of the symmetric mode and that of dominant mode:Usang, Ishizuka, Ivanyuk and SC "Correlated transitions in TKE and mass distributions of fission fragments described by 4-D Langevin equation", Scientific Reports 9, 1525(2019).

Importance of dynamical treatment

256Fm

258Fm

0.51.0

1.5

2.0

2.5

-40

-30

-20

-10

0

10

-0.6-0.4

-0.20.0

0.2 0.4 0.6

Ede

f (MeV

)

a

z0 / R

0

258Fm

0.51.0

1.5

2.0

2.5

-40

-30

-20

-10

0

10

-0.6-0.4

-0.20.0 0.2 0.4 0.6

256FmE def (M

eV)

a

z0 / R

0

24

25

256Fm 258Fm Scission Point Model

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Peak positions of FF in broader region of compound mass number

AL～132

AH～140

Anomalies in Fm, Md

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Itkis et al., Nucl. Phys. A944(2015)204-237Our calculation (4D Langevin)

Comparison with experimental data (right)

Exp.

No parameter is adjusted

Fragment shape at scission

• Estimation of deformation energy is now possible

• Spin and parity distribution?28

Z=120 SHE formation: Morimoto-san’s talk in Hawaii 2018

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CN formation

Touching process

Quasi fission

SHE formation process and theories available at Tokyo Tech.

SHE formationFusion-Fission

AMD,Cb-TDHFB

Langevin

Multistep Hauser-Feshbach Theory

Composite system

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CN formation

Touching process

Quasi fission

SHE formation process and theories available at Tokyo Tech.

SHE formationFusion-Fission

AMD,Cb-TDHFB

Langevin

Multistep Hauser-Feshbach Theory

Composite systemSHE touch CNF survP Ws s= × ×AMD, TDHF, VUU

LangevinMultistep Hauser-Feshbach

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Antisymmetrized Molecular Dynamics︓AMD

Mean Field + Stochastic NN collision

Total wave function：Single Slater det.

time-dependent variational principle

→ Equation of motion:evolution of mean field

𝑟 𝜙F1 =2𝜈𝜋

JKexp −𝜈 𝑟 −

𝑍>𝜈

7

𝜒>Single particle w.f.：Gaussian coherent state:

| ⟩𝛷 𝑟6, 𝑟7, … , 𝑟U =1𝐴!det 𝜙> 𝑟:

𝑖ℏ[:\

𝐶>^,:\ ̇𝑍:\ =𝜕ℋ𝜕𝑍>^∗

Stochastic NN collisionlike in cascade model (nearest Distant model)gives rise to branching of wave function→distribution

Akira ONO et al, Progress of Theoretical Physics, Vol. 87, No. 5 (1992)

⟩| ⟩|⟩|⟩|

𝑍 = 𝜈𝐷 +𝑖

2ℏ 𝜈𝐾,

ℋ = ⟨e|fg| ⟩e⟨e| ⟩e , 𝐶>^,:\ =

𝜕7

𝜕𝑍>^∗ 𝜕𝑍:\𝑙𝑜𝑔 𝜙> 𝜙:

𝜒> = 𝑝 ↑, 𝑝 ↓, 𝑛 ↑, 𝑛 ↓

𝜎, 𝜏 = {𝑥, 𝑦, 𝑧}Effective interaction：SLy4

32

b = 3.12 fmb = 0.03 fm

60Mn+242Am 53V+249Bk

Trial calculation：54Cr (310MeV) + 248Cmby AMD

33

54Cr (324MeV)+248Cm→302120

Touching process（b=0）by AMD

Dynamical large-scale reconfiguration of single-particle orbits is taking place. The fates of these 2 events are different due to stochasticity brought by the NN collision : TDHF is a deterministic theory 34

Shape at the 2nd minimum

302120

max

max

' ' ' ' ' '0' { , }: ' '

'' '' '' '' '' ''0'' { , , , , , , , }: '' ''

( , ) ( )

( , ) ( )

x

x

nE Jx l j x

n l jE J

x l j xn p d t h F l j

E J T E dE

E J T E dE

pa a

a g

pa a

a a g

r

r=

=

é ùê ú

= ê úê úê úë û

å ò

å ò

CNF or Quasi FissionTouching processLangevin cal. with neutron evaporation

σtouch

PCNF

CN

α

Survival probability Wsurv

Cassini Ovaloid

Starting point of Langevin cal.

Shape profileU*, L

Edef(M

eV

)

AMD, Cb-TDHFB, VUUMicroscopic theories

BeOH+HFBTHO

({ }, , )PES q T L

Hybrid model of SHE formation of Tokyo Tech.

Multistep Hauser-Feshbachcalculation for Wsurv：

35

1 4{ , , }a a a

aÛ

Quasi Fission

N, Z, U*,J

Langevin calculation：E*=50MeV for 302120• Shape parametrization : Cassini ovaloid• Dynamical variables : 3 (α,α1,α4)• Transport coefficients：Linear Response Theory• Free energy surface : Woods-Saxon model （Pashkevich)• Washing out of shell effects： taken into account• Neutron emission：Iljinov et al., （Nucl. Phys. A 543, 517 (1992)）

• Rotational energy：taken into account

• Langevinequation:

,

1 .2

q p

Fp p p pq q

b bn n

nhb n h bn nh h bn n

b b

µµ

g µ q x

=

¶¶= - - - +

¶ ¶

!

!

ò-

--+

=G nn BU

nnninvnn

n EdEEBUEUms

000

2 )()()()(

)12( rsrp!

( ) 2n nP t tttD D

D = = G!

1Mµ -º

36Neutron emission probability at each time step:

Neutron emission Width:

PCNF

Multistep Hauser-Feshbach decay calculation

37Z, A-1Z, A

R(J)

Ener

gy

Sn(A)

Sn(A-1)

Z, A-2

G(Ex)

Spin

: Okumura, Kawano, SC. J. Nucl. Sci. Technol., 55,1009-1023(2018).

'max

''max

' ' ' ' ' ' '0' { , }: ' '

'' '' '' '' '' '' ''0'' { , , , , , , , }: '' ''

( * , ) ( )

( * , ) ( )

nE Jl j

n l jE J

l jn p d t h F l j

U S E J T E dE

U S E J T E dE

b

b

pb b b b b

b g

pb b b b b

b a g

r

r=

=

é ù- -ê ú= ê úê - - úê úë û

å ò

å ò

Wsurv

ρ：Level density（Kawano-Koura-Chiba）JNST 43, 1-8(2006).

T : Transmission coefficientsn～α：optical model

γ：Kopecki-Uhl EGLO(up to E3)Fission：Double-humped Hill-Wheeler

• Fission barrier：Litnevsky et al., PRC 89, 034626(2014)

• GS spin and parity：HFBTHO code (blocking method)

• Multichance fission automatically included

BeoH

*U

# of emitted neutrons

0n 1n 2n 3n 4n

Residue 302120 301120 300120 299120 298120

<U*> (MeV)

50 39.7 32.3 23.6 17.1

① PCNF 7.54×10-4 7.87×10-5 3.41×10-5 2.33×10-6 5.79×10-9

Bf (MeV) 3.12 3.61 4.02 4.61 6.92

②Wsurv 1.87×10-8 1.30×10-7 1.18×10-6 9.71×10-6 1.70×10-5

PCNF×Wsurv 1.41×10-11 1.02×10-11 4.02×10-11 2.26×10-119.84×10-14

Results from AMD+Langevin＋HF

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PCNF : Langevin

Wsurv: Multiste

p

Hauser-Feshbach

PCNF ・Wsurv

CN formation

Touching process

Quasi fission

SHE formation process and theories available at Tokyo Tech.

SHE formationFusion-Fission

Composite system

39

410CNFP -»

10[mb]touchs ～

120 0.1 10[fb]Zs = » ～

9 710 10survW - -» ～

13 1110 10CNF survP W - -× » ～

3-D Langevin

Multistep Hauser-Feshbach

AMD

This estimate depends much on input parameters, especially to fission barriers.More information is highly required.

In good agreement with estimation by Sekizawa-Hagino

# of emitted neutrons

0n 1n 2n 3n 4n

Residue 302120 301120 300120 299120 298120

<U*> (MeV)

50 39.7 32.3 23.6 17.1

① PCNF 7.54×10-4 7.87×10-5 3.41×10-5 2.33×10-6 5.79×10-9

②Wsurv(Bf:-0.5MeV)

4.85×10-10 5.38×10-9 7.55×10-8 9.10×10-7 2.24×10-6

PCNF×Wsurv

①×②3.66×10-13 4.23×10-13 2.57×10-12 2.12×10-121.30×10-14

Results from AMD+Langevin＋HF

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0.5MeVf fB B® -

Difference of 0.5 MeV in fission barrier changessurvival probability by 2 orders of magnitude

Concluding remarks1. Tokyo-Tech. 4-D Langevin model for nuclear fission has

been revealing origin of systematical and anomalous trends in mass and TKE distributions of fission fragments in terms of the transition of symmetric components from super long to super short as well as transition of the dominant mode

2. We have applied the methodologies we have developed for fission study to formation of Z=120 super heavy elements. It will be an independent important alternative to the more orthodox (mainstream) methods

3. We have been providing nuclear data, including fission fragment yields, neutron cross sections and ranching ratios to r-process community (Kajino-san, Wanajo-san, Hayakawa-san, Suzuki-san ..) I hope such collaboration would yield excellent new outcomes 41

C.Ishizuka1, M.D.Usang1,2, Y.Ishii1, S. Okumura1,3, S. Ebata1, T. Inakura1, F.A. Ivanyuk1,4, V.Litnevsky1,5,

A. Ono6, M. Kimura7

J.Y.Lee and S.W.Hong8

T.Kajino, T.Hayakawa, T.Suzuki, S.Wanajoand many others

1. Tokyo Institute of Technology

2. Malaysian Nuclear Agency

3. International Atomic Energy Agency

4. Institute of Nuclear Research, Kiev, Ukraine

5. Omsk State Transport University, Russia

6. Tohoku University

7. Hokkai University

8. Sungkyunkwan University

Collaborators

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Thank you very much!!

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