F. MinatoA, S. ChibaA, K. HaginoB

A. Japan Atomic Energy AgencyB. Tohoku Univ.

Fission barrier of uranium including Λ hyperon

Nucl.Phys.A831, 150 (2009) Nucl. Phys. A856, 55 (2011)

１． Λ impurity effects２．Motivation ３． fission barrier & density distribution４． Summary

Table of Contents

Λ Impurity effect

H. Tamura et al., NPA 754, 58(2005)

• Levelexperiment

T. Motoba et al., Prog. Theor. Phys. 70, (1983) 189.E. Hiyama et al., Phys. Rev. C 59, (1999) 2351.

αp

n

Rcore-(np)de

nsity

dist

ributi

on

• Shrinkage

Rcore-(np)

6Li

cluster model

peak at E= 12.8 MeV

Dipole motion of 18ΛΛO

FM&KH, Physical Review C 85, 024316 (2012)

Λ [1p(1s)-1] 80 %n&p [1d5/2(1p3/2)-1] 20%

Λ Impurity effect RPA with degree of freedom of Λ

1) production of Λ in nuclei

High energy is released in production & decay of Λ

Fragment distribution after Λ weak decay in 138

53I

change of “final” fission yield

⇒ promote Fission & destruction of Fission Product

Λ + N N + N + 190 MeVK- + 238U 239ΛU + π- + 178 MeV

2) decay of Λ in nuclei

Motivation What is impurity effect like in Λ hyper-actinide?

Λ life-time ~10-10 sec

Fission of Hyper-uranium

T.A.Armstrong, J.P.Bocquet, G.Ericsson, et al. Phys. Rev. C 47, 1957 (1993).

H.J. Krappe and V.V. Pashkevich, Phys. Rev. C 47, 1970 (1993).

F.F. Karpeshin, C.G. Koutroulos, M.E. Grypeos, Nucl. Phys. A595, 209 (1995).

H.J. Krappe and V.V. Pashkevich, Phys. Rev. C 53, 1025 (1996).

Theory

Fission barrier of Hypernuclei ??

Experiment

heavy fragment

Λ-att

achm

ent

prob

abili

ty

light fragment

M. Rayet, Nucl. Phys. A367 (1981) 381

◆ΛN interaction

Skyrme-Hartree-Fock

◆ΛΛ interaction

2. quadrupole constraint

1. reflection asymmetry

Skyrme-type interaction for ΛN & ΛΛ interaction

zr

9 parameters: t0Λ, x0

Λ, t1Λ, t2

Λ, t3Λ, λ0, λ1, λ2, λ3

Lanskoy PRC58, 3351(1998)

SkM* parameter setNN interaction:

λ0 (MeV fm3)

λ1 (MeV fm5)

range μ (fm)

SΛΛ1 -312.6 57.5 0.61

SΛΛ3 -831.8 922.9 1.49

1. ΔBΛΛ(13BΛΛ) = 4.8 or 0.6 MeV2. λ2=λ3 = 0

ΛΛ :

Skyrme-Hartree-Fock

ΛN :

Y. Yamamoto, H. Bando, and J. Zofka, Prog. Theor. Phys. 80, (1988) 757.

1. B.E. of 5ΛHe and 209

ΛPb 2. m*

Λ/mΛ =0.8 in nuclear matter 3. energy difference between 0+ and 1+ of 4

ΛHe4. W0

Λ=0

Λ bond energy ΔBΛΛ=BΛΛ-2BΛ

YBZ4 set: t0Λ=-315.3, t1

Λ=23.14, t2Λ=-23.14, t3

Λ=2000, x0Λ=-0.109

range of “equivalent” single gaussian potential

Lanskoy PRC58, 3351(1998)

cf. FM & SC Nucl. Phys. A856, 55 (2011)

↑0.53

0.27↑

Fission barrier height

0.61-0.63↑

↑0.91-1.03

x 2

Result

single-Λ 239ΛU double-Λ 240

ΛΛU

Core Energy Λ Energy

0.25

Change of Core EnergySMALL

Energy of Λ particle increases due to transfer to fragment with smaller mass

0.5

Why Increase of Bf?

238U 239

ΛU

ground state outer barrier Q2=200 barn

Λ particle moves to heavier fragment

Density distribution of 239ΛU

Density distribution of 240ΛΛU

FM & SC Nucl. Phys. A856, 55 (2011)

CORE

Λ(SΛΛ1)range

μ=0.61fm

Λ(SΛΛ3)range

μ=1.61fm

ground state Q2=200 barn

SUMMARY

Inner Bf : 0.27 MeV↑Outer Bf : 0.50 MeV↑

Λ particle(s) move to heavier fragment in adiabatic approximation

Calculate Fission Barrier height & density distribution of 239

ΛU, 240ΛΛU

with Skyrme-Hartree-Fock approach◆Fission barrier height

Inner Bf : 0.61~0.63 MeV↑Outer Bf : 0.91~1.03 MeV↑

Barrier height is increased

◆Density distribution