Common Nuclear Data Problems for Fission Cycling in r-process

and Nuclear Energy

S. Chiba

JAEA

Fission (cycling) in r-process nuFission (cycling) in r-process nucleosynthesiscleosynthesis

• Discovery of Ｔｈ and Ｕ in metal poor stars

• For realistic calculation of r-process nucleosynthesis– Is there a termination point? 　 Where is that?– Possibility of SHE generation and discovery of its

relics in meteorites– Impacts on universality (56 Z 75)≦ ≦– Impacts on nucleo-cosmochronometers

• Th/Eu, U/Th, Th/Os,....

Supply to m

edium-weight

region by fiss

ion, which

is

less se

nsitive

to th

e

physica

l conditio

ns of r-

process

sites

Continuous f

low

from th

e bottom

S=250

132Sn

208Pb

238U

Regions where fissions take Regions where fissions take place in terms of KTUY05place in terms of KTUY05

Competing processes in calculation Competing processes in calculation of fission cyclingof fission cycling

• Spontaneous fission• Neutron-induced reactions

– Neutron-capture and inverse reaction– Neutron-induced fission FFMD

• β-decay– β-delayed fission FFMD– β-delayed neutron emission

• ν-induced reactions– (ν,e-xn) reaction– (ν,f) FFMD

30y 18.1y

235U 236U 237U 239U238U234U

237Np 238Np 239Np

238Pu 239Pu 240Pu 241Pu 242Pu 243Pu

241Am 242Am 243Am 244Am

242Cm 243Cm 244Cm 245Cm

注）青字は核分裂性核種（核分裂断面積が捕獲断面積の 3倍以上）

2.12d

236Np

87.8y

14.9y

6h(0.16)

242mAm

16h(0.84)

4.96h

2.36d

注）赤字は主要MA核種　　　（いずれも非核分裂性核種）

10.1h

163d

152y

注）青→は、数日以内の　　短期的崩変

2.25h 6.75d

出典）　オーム社「原子力ハンドブック」および　　　　　高速炉用ORIGEN2断面積ライブラリ（ JENDL3.3）

23.5m

Burn-up of Actinides in Nuclear Reactors

Critical mass of 235U with various moderators

曲線上の数値は [ 減速材原子（分子）数 ]/[235U 原子数 ] を表す

Dynamical network calculationDynamical network calculationTerasawa et al., ApJ 562, 470(2001)

originally from Prof. Meyer ??

• Reaction rates 　– Thielamann , Caughlan-Fowler, Maleney-Fowler, Fowler-Hoyle, Rausch

er, Mohr, Wagoner, Kajino-Boyd, Orito-Kajino-Mathews, Kajino-Fukugita,Ohsaki, NACRE96

• Nuclear mass– Hilf-Groote-Takahashi (modified) KTUY05 (Prog. Theor. Phys. 305 （ 200

5 ） 113)• β-decay rates

– Klapdor GT-2 with KTUY05 mass, including 1n emission(2007)• ν-induced spallation rate (A(ν,e- xn)A') (x=0, 8)

– Langanke (5 Z 100) ≦ ≦ with dumping• no fission mode ⇒β-delayed fission, spontanious fission(KTUY05)• α-decay (KTUY05 mass)• Data on expanding matter of SNeII : numerically read ⇒ exponential model

Exponential model for Exponential model for expanding nuclear matterexpanding nuclear matter

c.f. General-relativistic hydro-dynamical simulation by Terasawa, Kajino, Sumiyoshi et al. (ApJ 562, 470(2001)) （ dots ）

lower 2 lines : T9

upper 2 lines : density

Exponential model

S

tTt

msttT35 )(91033.3

)(

7.0)7/exp(4.8)(9

Ye=Yp=0.427

Entropy-dependence of r-Entropy-dependence of r-process abundanceprocess abundance

β-delayed fissionβ-delayed fission ：： Bf-dependenceBf-dependence

(KTUY-3MeV（ left）、MS96（ right） )

FFMD (Konan model):FFMD (Konan model):248248Cm, Cm, 236236UU

β-delayed fissionβ-delayed fission ：： FFMD-dependenceFFMD-dependence

En

JJππ-dependence of CN decay-dependence of CN decay

target

Compound

TS-1 TS-2

PES

deformation (elongation)

Ex

Bn

Tn Tγ

Jπ

Jfo

Jfi

Jfo

JfiJ

fTT

TTT

JfiT J

foT

Bfi Bfo

β-decay, ν- 反応

Jπ-dependence of compound formation c.s.

s 波

p 波

d 波

Decay width

dUETJT fi

U

HWTSiJfi )(),,(

0

nn BEU

U

JBAc dUTT J

0

)()(

nE

JnOMTJn dETT

0

)()(

Brink-Axel

Hill-Wheeler

Optical modelTarget

Compound

Transition state

TTT

TB

nf

xx

Fission Probability

• Very strong Jπ-dependence

• No-experimental evidence

• How can we verify it ？– Various projectile ？ (d,

3He, 18O)

Level density on the saddle

• How to verify it ？

Nuclear Structure Effects ： SRM-CC

• 238U + n• Coupling scheme : G.S. b

and (0+ - 2+ - 4+ - 6+ - 8+)+4 side bands

• Soft Roator Model prediction of coupling strengths

• OMP : E.S. Soukhovitsij, S. Chiba et al., J. Phys. G. 30, 905-920(2004).

(coupled-levels)

Effects of low-lying levels on reaction c.s.

G.S. Band

BBnn of Sn isotopes and HF, DSD c.s. of Sn isotopes and HF, DSD c.s.

UU 同位体の同位体の BBnn

State-dependence of DSD c.s.State-dependence of DSD c.s.

ResonancesResonances

Effects of resonances on MACS

Summary

• There are many ambiguities in calculation of β-delayed fission rates, neutron-induced fission rates necessary for fission cycling– Fission barriers, level density (especially at the saddl

e), their Jπ-dependence, FFMD, deformation parameters and GDR parameters

• Neutron binding energies affect the relative magnitude of DSD and HF cross sections

• DSD c.s. is sensitive to the presence and energies of the p-states

• Nuclear structure (low-lying levels) is important for reaction c.s. calculation