1. F. Minato A, S. Chiba A, K. Hagino B A. Japan Atomic Energy Agency B. Tohoku Univ. Fission barrier of uranium including Λ hyperon Nucl.Phys.A831, 150 (2009)Nucl. Phys. A856, 55 (2011)

2. １． Λ impurity effects ２． Motivation ３． fission barrier & density distribution ４． Summary Table of Contents

3. Λ Impurity effect H. Tamura et al., NPA 754, 58(2005) Level experiment T. Motoba et al., Prog. Theor. Phys. 70, (1983) 189. E. Hiyama et al., Phys. Rev. C 59, (1999) 2351. α p n R core -(np) density distribution Shrinkage R core -(np) 6 Li cluster model

4. peak at E= 12.8 MeV Dipole motion of 18 ΛΛ O FM&KH, Physical Review C 85, 024316 (2012) Λ [1p(1s) -1 ] 80 % n&p [1d 5/2 (1p 3/2 ) -1 ] 20% Λ Impurity effect RPA with degree of freedom of Λ

5. 1) production of Λ in nuclei High energy is released in production & decay of Λ Fragment distribution after Λ weak decay in 138 53 I  change of “final” fission yield ⇒ promote Fission & destruction of Fission Product Λ + N  N + N + 190 MeVK - + 238 U  239 Λ U + 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

6. 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-attachment probability light fragment

7. 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 z r 9 parameters: t 0 Λ, x 0 Λ, t 1 Λ, t 2 Λ, t 3 Λ, λ 0, λ 1, λ 2, λ 3 Lanskoy PRC58, 3351(1998) SkM* parameter set NN interaction:

8. λ 0 (MeV fm 3 ) λ 1 (MeV fm 5 ) range μ (fm) SΛΛ1-312.657.50.61 SΛΛ3-831.8922.91.49 1.ΔB ΛΛ ( 13 B ΛΛ ) = 4.8 or 0.6 MeV 2.λ 2 =λ 3 = 0 ΛΛ : Skyrme-Hartree-Fock ΛN : Y. Yamamoto, H. Bando, and J. Zofka, Prog. Theor. Phys. 80, (1988) 757. 1. B.E. of 5 Λ He and 209 Λ Pb 2. m * Λ /m Λ =0.8 in nuclear matter 3. energy difference between 0 + and 1 + of 4 Λ He 4. W 0 Λ =0 Λ bond energy ΔB ΛΛ =B ΛΛ -2B Λ YBZ4 set: t 0 Λ =-315.3, t 1 Λ =23.14, t 2 Λ =-23.14, t 3 Λ =2000, x 0 Λ =-0.109 range of “equivalent” single gaussian potential Lanskoy PRC58, 3351(1998) cf. FM & SC Nucl. Phys. A856, 55 (2011)

9. ↑ 0.53 0.27↑ Fission barrier height 0.61-0.63↑ ↑ 0.91-1.03 x 2 Result single-Λ 239 Λ U double-Λ 240 ΛΛ U

10. Core Energy Λ Energy 0.25 Change of Core Energy SMALL Energy of Λ particle increases due to transfer to fragment with smaller mass 0.5 Why Increase of B f ? 238 U 239 Λ U

11. ground stateouter barrier Q 2 =200 barn Λ particle moves to heavier fragment Density distribution of 239 Λ U

12. Density distribution of 240 ΛΛ U FM & SC Nucl. Phys. A856, 55 (2011) CORE Λ(SΛΛ1) range μ=0.61fm Λ(SΛΛ3) range μ=1.61fm ground state Q 2 =200 barn

13. SUMMARY Inner B f : 0.27 MeV↑ Outer B f : 0.50 MeV↑ Λ particle(s) move to heavier fragment in adiabatic approximation Calculate Fission Barrier height & density distribution of 239 Λ U, 240 ΛΛ U with Skyrme-Hartree-Fock approach ◆ Fission barrier height Inner B f : 0.61~0.63 MeV↑ Outer B f : 0.91~1.03 MeV↑ Barrier height is increased ◆ Density distribution