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A systematic TDDFT data for analysis

岩田順敬 (Yoritaka Iwata) 東工大 科学技術創成研究院 (Tokyo Tech)

with T. Nishikawa (, Ltd) K. Kean (Tokyo Tech. and JAEA) S. Chiba (Tokyo Tech.)

Introduction on nuclear chart

Fission mechanism is studied for this region

Nucleus in our scope Thermal Fission CS We have less information about the fissility

BE/A

Halflife

236 U Motivation

◇ Nuclear fission is one of theoreticallytheoretically difficult processes in sub-atomic physics.

DifficultDifficult toto treattreat microscopicallymicroscopically

HereHere wewe taketake lessless phenomenologicalphenomenological (ab-initio(ab-initio like)like) treatmenttreatment suchsuch asas TDDFTTDDFT (time-dependent(time-dependent densitydensity functionalfunctional theory).theory).

◇◇ InIn termsterms ofof fission,fission, twotwo topicstopics areare focusedfocused onon ……

__ many-bodymany-body forceforce

__ frictionfriction andand dissipationdissipation Fission dynamics mapped on Eq. of Motion Γ(t) :random force macroscopic

Potential V Friction γ … by CHF … by TDDFT microscopic TDDFT calc.

R Contents

◇ CHF for FissionFission barrierbarrier heightheight SLy4SLy4 byby Kean-Iwata-ChibaKean-Iwata-Chiba

…… effectiveeffective many-bodymany-body forceforce effecteffect

◇ TDDFT + Langevin model for Friction by Nishikawa-Iwata-Chiba

…… effectiveeffective dissipationdissipation includedincluded inin TDDFTTDDFT SV-basSV-bas ◇ Result Theoretical Nuclear data … provided by theoretical systematics

◇ Summary Density functional theory

WHY microscopic ?

degree of freedom ( Fermi statistics )

➔ Nucleon-nucleon interaction ( incl. spin-orbit force ) ➔Mean-field type description ➔ Coulomb force nucleus

➔ Less phenomenological Less free parameter (no free parameter for dynamics)

ーーーーーー ➔TDDFT and CHF use the same functional form

neutron Fission dynamics to refine fissility ... mapped on Eq. of Motion Γ(t) :random force macroscopic

Potential V Friction γ … by CHF … by TDDFT FissilityFissility microscopic TDDFT calc.

R ~ 50 ◇ CHF for FissionFission barrierbarrier heightheight

FissionFission barrierbarrier heightheight byby constraintconstraint Hartree-FockHartree-Fock withwith pairingpairing (density(density dependentdependent pairing)pairing)

15 236UU

]

]

V V 10

e

e

M M α = 1/6 [

[

E E 5

SLy4SLy4 ββ=Q=Q20 0 0 0.2 0.4 0.6 0.8 1 1.2

SinceSince thethe barrierbarrier heightheight isis examinedexamined byby β,β,

onlyonly symmetricsymmetric fissionfission cancan bebe identifiedidentified ([Thr.]([Thr.] barrierbarrier heightheight becomesbecomes ratherrather higher).higher). Fission barrier height

We need a reliable fission barrier

inner barrier (outer barrier)

Fission barrier height is 4 to 7 MeV (exp.), while they are calculated from 7 to 14 MeV (SLy4).

… almost twice larger

The improved interaction is necessary !

_ why are most of the Skyrme interactions so large ?

_ is there any way to re-fit the Skyrme interaction ?

in the corresponding part of nuclear chart Medium effect force effect

Hamiltonian density of density functional theory

Analogous to

Alpha term: density dependent term

on the fission barrier height ... Perturbation analysis for alpha-effect

15

236UU 10

α = 1/6

5 alpha value +10 % SLy4SLy4 ββ=Q=Q20 0 20 0 0.2 0.4 0.6 0.8 1 1.2

[Perturbation analysis] -10 % We examined 10 % different cases starting from

Original alpha = 1/6 = 0.1666... Sensitivity of fission barrier height on alpha

We have confirmed

Only 10 % change of a … can contribute to … ~40% difference of fission barrier height

This fact is confirmed in

U- 231 to 239 Pu-isotopes 237 to 245 using SkM*, SLy4, SV-bas interactions. alpha value -10 % Alpha-perturbation theory This fact is our motivation to change alpha slightly to have a better description of fission barrier height What to change [Strategy] +10 %

Also change this one to keep the total contribution as a whole term Validity of the proposed method

Binding [MeV] Original calc (Proposed calc)

Original Proposed

Radius [fm] RIPL3 r_p, r_n, r_tot (r_p, r_n, r_tot)

Only small deference in these values (quality is kept) Correlation between experimental and theoretical results for SLy4 and SkM* interactions

● original

● proposed

Theoretical database I using substantially refined Skyrme forces

…m-SLy4 m-SkM* m-SV-bas in terms of fission

◇ TDDFT + Langevin model

Friction along the collision axis Process of extracting friction effect Model time evolution

Duration time ~ 1.5 [10-21 s] 296116 = 296Lv symmetric fission by TDDFT

R

Y.Iwata and S. Heinz, CERN Proceedings 002 (2012)

Averaged friction coefficient Microscopic inputs

R, dR/dt : extracted

◇ TDDFT + Langevin model

It should play a essential role in fission

Friction along the collision axis Validity for TDDFT + 4D Langevin method

236UU

This is good enough (more than expected), now we engage to calculate the other cases Linearly scaled energy-dependence

← Root-mean squared line

This is not only for the U236, but for the other isotopes. Indeed ... [systematics] Linearly scaled energy-dependence

N=150 120 isotopes

100

80 Friction coeff. g

60

40 N=146 120 20 100 0 Energy 1 2 3 4 5 6 807 8 9 10 11

60

40 N=142 20 120

0 100 1 2 3 4 5 6 7 8 9 10 11

80

60

40

20

0 1 2 3 4 5 6 7 8 9 10 11 [systematics] Linearly scaled energy-dependence

N=152 140 isotopes 120

100

80 Friction coeff. g

60 40 N=148 20 120

0 100 1 2 3 4 5 6 7 8 9 10 11 Energy 80

60

40 N=144 20 140 0 120 1 2 3 4 5 6 7 8 9 10 11 100

80

60

40

20

0 1 2 3 4 5 6 7 8 9 10 11 [systematics] Linearly scaled energy-dependence N=154 120

100 Curium isotopes

80 Friction coeff. g 60 N=150 40 120 20 100 0 2 3 4 5 6 807 8 9 10 11 Energy 60

40

20 N=146 0 120 2 3 4 5 6 7 8 9 10 11 100

80

60

40

20

0 2 3 4 5 6 7 8 9 10 11 [Systematics] Linearly scaled energy-dependence

Modeled by ... γ = a (E/A) + b

b 115 120 125 130 135 140 145 -4.5

-5 U Pu [As a physical law] [As a physical law] Cm Cf

This would be the first time -5.5 Fm to show the energy a dependence of friction -6 using microscopic calculations -6.5 Statistical law

found by Nishikawa-san -7 Neutron number

Energy dependence is rather moderate compared to dependence in which Z dependence is larger than N dependence

Friction along the collision axis 236U

Similarity can be found in BE How does the friction behave ? Thermal Neutron Fission CS

Similarity can be found in BE/A

BE/A

Halflife

236 U Theoretical Database II (SV-bas and more) SkM* , SLy4 calcs will follow before long. SLy4

0.58 100 98 0.54 96

A 94 / γ 0.5 0 92

0.46 1.48 1.52 1.56 1.6 1.64

N/Z The model eq. for exploring Z=120

Stochastic 1D eq. to refine the fissility Γ(t) :random force

+ Coulomb pot

Potential V Friction γ … by CHF … by TDDFT microscopic TDDFT calc.

R Summary SkM*SkM* ◇ FissionFission barrier/Potentialbarrier/Potential SLy4SLy4 (mainly(mainly byby K.K. KeanKean sansan)) … Alpha-perturbation theory SV-basSV-bas

◇ Friction (mainly by Nishikawa san)

… Friction formula (depending on mass and energy)

These are substituted into both

_ 1D Langevin type equation (for refining fissility)

_ Usual 3D and 4D Langevin equation