Dynamical Model of Surrogate Reaction

1. Dynamical Model of Surrogate Reaction 1. Introduction Surrogate reactions 2. Model Unified model Trajectory analysis  Langevin equation Two center parametrization 3. Results 18O+238U  16O+240U J-distribution of compound nucleus Mass distribution of fission fragments Y. Aritomo, S. Chiba, and K. Nishio Japan Atomic Energy Agency, Tokai, Japan Dynamics and Correlations in Exotic Nuclei (DCEN2011) 20th Sep.-28th Oct. 2011, YITP, Kyoto, Japan

2. Surrogate ratio methods S. Chiba and O. Iwamoto, PRC 81, 044604(2010) Desired reaction n1 impossible Reaction n2 possible Rfn2 Rfn1 n n Jπ Jπ CN A CN B Short life Minor Actinide stable RfS1 RfS2 Jπ Jπ HI HI Target(1) CN A Target(2) CN B Surrogate reaction S1 possible Surrogate reaction S2 possible

3. Chiba-Iwamoto condition  Surrogate Ratio Method 1. Spin of CN is less than 10 hbar 2. Spin distribution of two reactions  similar S.Chiba and O. Iwamoto, PRC 81,044604(2010) 18O + 238U  16O + 240U

4. Study of Surrogate reactions at JAEA • 　　　■ Experiments • Tandem accelerator • Silicon detector, MWPC • 　　　■ Theoretical study • Transfer process • Classical approach • Langevin calculation • Quantum mechanical approach • CDCC • Decay process • Statistical approach • Dynamical approach ΔE - E MWPC

5. 16O 18O t > 10-21 sec Vdiabatic Vadiabatic Initial condition Deformation Momentum Angular momentum Excitation energy 238U 240U β2=0.0 β2=0.2 z : c.m distance α mass asymmetry 256Fm nucleon transfer 18O + 238U  16O + 240U 240U Decay process of compound nucleus Y. Aritomo, S. Chiba, and K. Nishio, PRC 84, 024602 (2011)

6. 2. Model • 2-1. Potential • 2-2. Equation Time-evolution of nuclear shape in fusion-fission process

7. Calculation with Unified Model Diabatic and Adiabatic Potential Energy Starting from the infinite distance between the target and projectile Treat all process （unified potential） （unified equation） Unified Model (FLNR group) V. Zagrebaev, A. Karpov, Y. Aritomo, M. Naumenko and W. Greiner, Phys. Part. Nucl. 38 (2007) 469 Time dependent weight function G. F.Bertsch, 1978;  W.Cassing, W.Nörenberg,1983.A. Diaz-Torres, 2004; A. Diaz-Torres and W. Scheid, 2005.

8. Nuclear shape two-center parametrization (Maruhn and Greiner, Z. Phys. 251(1972) 431) δ=0 (δ1=δ2 ) Trajectory which enters into the spherical region = fusion trajectory c.m. distance z mass asymmetry

9. Langevin type equation Before touchingnucleon transfer mij : Hydrodynamical mass (mono-nucleus region), Reduced mass (separated region) γij: Wall and Window (one-body) dissipation

10. Transfer Ptr : one nucleon transfer probability depended on surface distance bewteen the both nuclei V.I. Zagrebaev, Phys. Rev. C67, 061601 ( R) (2003) V.I. Zagrebaev and W. Greiner, J. Phys. G31 825 (2005)

11. Outline : Classical description • Nucleus as Liquid drop • Classical model trajectory calculation with friction γtan J distribution Classification of reactions by impact parameter Spin distribution of compound nucleus

12. 3-2 Resulttransfer process 18O + 238U  16O + 240 UEcm=133.5 MeV J distribution of compound nucleus by two nucleons transfer reaction 10-22MeV s fm-2 Spin of compound nucleus  less than 10 Surrogate ratio methods Chiba-Iwamoto condition (1)  OK S.Chiba and O. Iwamoto, PRC 81, 044604(2010)

13. 3-3 Resulttransfer process J distribution of compound nucleus by two nucleons transfer reaction 18O + 238U 16O + 240U 18O + 236U 16O + 238U Ecm=133.5 MeV J-distribution of two reactions  similar 5 x 10-22MeV s fm-2 Surrogate ratio methods Chiba-Iwamoto condition (2)  OK γ= 5×10-22MeV s fm-2 S.Chiba and O. Iwamoto, PRC 81, 044604(2010)

14. 3 Results sliding friction dependence 18O + 238U 256Fm*fission, Ecm=133.5 MeVMDFF Units of friction 10-22MeV s fm-2 ・ Exp. data Nishioet.al. （JAEA）

15. 4. Application to Surrogate reaction Exp. impossible Coupled Channel Fission fragments Mass distribution Angle distribution Short life Minor Actinide Compound nucleus J Fission fragments Mass distribution Angle distribution Fission fragments Mass distribution Angle distribution Compound nucleus J Exp. possible We can treat using Langevin calculation with nucleon transfer

16. Test decay process of CN 240U E*= 40 MeV Initial condition Deformation Momentum Angular momentum Excitation energy α mass asymmetry z : c.m. distrance α mass asymmetry 3-dim Langevin calculation shell correction energy fission at low excitation energy z: c.m. distance Konan Gr. FLNR th Gr.

17. 3-4 MDFF: E* < 20 MeVNishioet al. New

18. Calculation（fluctuation-dissipation model ＋ TCSM） Yield (%) Fragment Mass (u) ・Exp. data：Nishioet.al. （JAEA） --- Calculation S. Chiba, O. Iwamoto and Y. Aritomo, PRC in print

19. 240U（E*= 10 MeV） J-dependence of MDFF J＝０ J＝１０ J＝２０ （％） S. Chiba, O. Iwamoto and Y. Aritomo, PRC in print Mass

20. 4. Summary 1. Surrogate reactions are described using unified model, which can treat transfer reaction and decay processes. 2. We obtained the spin distribution of the compound nuclei  surrogate reactions. Surrogate ratio method (Chiba-Iwamoto condition） 1. Spin of CN is less than 10 hbar 2. J distribution of two reactions  similar  satisfied within this calculation(18O+238U 16O+240U Ecm=160MeV) 3. In the unified model, we can compare the calculation results with the experimental data directory. • (Mass distribution of fission fragments, angle of ejected particle, kinetic energy loss, charge distribution of fission fragments) •  adjusting the unknown parameters 4. Future study charge number and neutron number symmetries  mass asymmetry deformations of each fragments description of fission process of low excited CN, with high accuracy.