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

Desired reaction n1 impossible Surrogate ratio methods Reaction n2 possible JπJπ JπJπ JπJπ JπJπ CN A CN B n n HI Target(1 ) Target(2 ) Rfn1Rfn1 RfS1RfS1 Rfn2Rfn2 RfS2RfS2 stable Short life Minor Actinide Surrogate reaction S1 possibleSurrogate reaction S2 possible S. Chiba and O. Iwamoto, PRC 81, (2010)

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

■ Experiments 1. Tandem accelerator 2. Silicon detector, MWPC ■ Theoretical study Transfer process 1. Transfer process 2. Classical approach Langevin calculation 1. Quantum mechanical approach CDCC Decay process 1. Decay process 2. Statistical approach 3. Dynamical approach 4. Study of Surrogate reactions at JAEA MWPCΔE - E

18 O 238 U 16 O 240 U Y. Aritomo, S. Chiba, and K. Nishio, PRC 84, (2011) 256 Fm nucleon transfer 240 U Decay process of compound nucleus t > sec V diabatic V adiabatic β 2 =0.0β 2 = O U  16 O U

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

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

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

Langevin type equation m ij : Hydrodynamical mass (mono-nucleus region), Reduced mass (separated region) γ ij : Wall and Window (one-body) dissipation Before touching nucleon transfer

Transfer V.I. Zagrebaev, Phys. Rev. C67, ( R) (2003) V.I. Zagrebaev and W. Greiner, J. Phys. G (2005) P tr : one nucleon transfer probability depended on surface distance bewteen the both nuclei

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

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

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

18 O U  256 Fm *  fission, Ecm=133.5 MeV MDFF 3 Results sliding friction dependence Units of friction MeV s fm -2 ・ Exp. data Nishio et.al. （ JAEA ）

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

Test decay process of CN 240 U E*= 40 MeV Konan Gr. FLNR th Gr.

3-4 MDFF: E* < 20 MeV Nishio et al. New

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

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

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 ( 18 O+ 238 U  16 O+ 240 U Ecm=160MeV) 3. In the unified model, we can compare the calculation results with the experimental data directory. 1. (Mass distribution of fission fragments, angle of ejected particle, kinetic energy loss, charge distribution of fission fragments) 2.  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. 4. Summary