Quasifission and dynamical extra-push in heavy and superheavy elements synthesis

Transcription

1 Humboldt Kolleg entitled "Interacting Structure and Reaction Dynamics in the Synthesis of the Heaviest Nuclei" Quasifission and dynamical extra-push in heavy and superheavy elements synthesis Lu Guo University of Chinese Academy of Sciences, Beijing 1

2 Outlines I. Introduction brief introduction of TDHF theory II. Discussions and results effect of spin-orbit force on dissipation dynamics role of tensor force in fusion reactions quasifission and extra-push dynamics III. Summary and outlook 2

3 Theoretical models in heavy-ion collisions Macroscopic model nucleus-nucleus potential (Bass model, Double folding ) coupled channels theories barrier penetration models... Microscopic model quantum molecular dynamics (QMD) time-dependent Hartree-Fock (TDHF)... Quantum effects are incorporated in a quantum mechanical way in TDHF, while was not well taken into account in QMD; Two-body collisions are included in QMD, while only one-body collision in TDHF; 3

4 TDHF theory: historical remarks Method was first applied by Bonche, Koonin, and Negele, fusion excitation function, fission, deep-inelastic collisions, nuclear molecules, collective excitation and resonance dynamics nonlinear giant resonance = RPA fusion deep inelastic collision 4

5 TDHF theory: historical remarks many groups in the late 70s and 80s performed more extensive calculations in 2 and 3 dimensions, limited by the computers of the time, e.g., K. T. R. Davies, V. Maruhn-Rezvani, K. R. Sandhya-Devi, S. J. Krieger, J. A. Maruhn R. Y. Cusson, H. Stöcker, J. A. Maruhn H. Flocard, M. S. Weiss most calculation in 2D axial geometry, no l*s-force (essential for correct shell structure) hindrance at the ECT*, Trento, Italy, Sep. 1-4,

6 The conflict between TDHF prediction and experimental data promotes the theoretical development puzzle of small fusion window 6

7 Spin-orbit coupling solved puzzle of small fusion window A. S. Umar, M. R. Strayer, and P.-G. Reinhard, Phys. Rev. Lett 56, 2793 (1986). Include time-even spin-orbit force Omission of l*s-coupling underestimated the energy dissipation so that the energy window of fusion reactions was too small in comparison with experiments. 7

8 Fusion window problem revisited M. Tohyama and A. S. Umar, Phys. Rev. C65, (2002). TDDM: time-dependent density matrix theory includes both one- and two-body collisions The l*s force has significant effect on the collision dynamics; The role of l*s force can be compensated by two-body collisions when l*s is absent; The increase in E th remains small due to two-body collisions when spin-orbit force was already included; 8

9 TDHF theory: advantages vs. limitations Three-dimensional TDHF with full Skyrme functional and without any symmetry restrictions; Advantages Fully microscopic, parameter-free theory in heavy-ion collisions; Treat nuclear structure and reactions in a unified framework (same EDF); Dynamical effects in heavy-ion collisions (neck formation, deformation, surface vibrations, nucleon exchange) are automatically incorporated; Quantum effects ( Pauli principle, antisymmetrization of wavefunction, spin-orbit force) are treated in a quantum mechanical way; Limitations Only one-body dissipation (collision with walls of mean-field); Tunneling effect is missing; 9

10 I. Importance of spin-orbit force 90 MeV 130MeV 170MeV The l*s force causes a significant enhancement of the dissipation; The energy dissipation decrease as c.m. energy increases owing to the competition of collective motion and single-particle degrees of freedom; G. F. Dai, LG, E.G. Zhao, and S.G. Zhou, Phys. Rev. C90, (2014). 10

11 I. Importance of spin-orbit force Around 40%~65% of the energy dissipation depending on the different Skyrme parameters is found to arise from the spin-orbit force in deep-inelastic collisions. 11

12 II. Effect of tensor force on fusion dynamics The effect of tensor force in heavy-ion collisions has been investigated. t v ( r ) t e 3( 1 ')( 2 ') ( 1 2 ) ' ( ) ( ) 3( 1 )( 2 ) ( 1 2 ) 2 k k k r r k k k t 3( k ') ( r )( k ) ( ) k ' ( r ) k o preliminary 12

13 II. Effect of tensor force on fusion dynamics P T T exp C C preliminary The inclusion of tensor force makes around 55%~15% better agreement with the experimental fusion cross sections.. 13

14 III. Fusion dynamics: extra-push and quasifission schematic figure for extra-push dynamics E cm E cm repulsive Coulomb interaction cohesive nuclear force An extra push --- An additional bombarding energy in the excess of Coulomb barrier --- quasifission 14

15 III. TDHF fusion threshold Our purpose is to investigate whether TDHF calculation will predict the need for an extra-push over the interaction barrier in order to make the heavier system fused. TDHF fusion threshold Coulomb barrier 16 O+ 208 Pb E lf : the low energy threshold for fusion 15

16 III. Interaction potential with EDF Our purpose is to investigate whether TDHF calculation will predict the need of extra push for heavier systems. TDHF fusion threshold Coulomb barrier Energy density functional (EDF) with Frozen density (FD) approximation--- Assume the densities of target and projectile remain constant and equal to their respective ground state densities. FD V ( R) [ ˆ ]( R) [ ˆ ] [ ˆ ] P T P T 16

17 III. Dynamical extra-push Reaction E TDHF lf V FD B V exp B R FD B R exp B 16 O+ 16 O O+ 40 Ca Ca+ 40 Ca Ca+ 48 Ca Ca+ 48 Ca O+ 208 Pb Ca+ 90 Zr TDHF results are in better agreement with experimental data 17

18 III. Fusion dynamics: extra-push and quasifission 48 Ca U 112Cn E lf =220MeV About 20 MeV extra-push energy is necessary in superheavy element synthsis due to quasifission. TDHF + statistical model (ongoing work) P W, P 1 P ER cap CN sur CN quasifission 18

19 16 40, , O Zr Ca Pb Sn Zn Zr Ca Pb Sn U 4zz ( z / A) 34, E(extra-push energy) 2.5* ( z / A) eff 1/3 1/3 1/3 1/3 A1 A2 ( A1 A2 ) eff We predict the need for an extra push over the interaction barrier in order to make the heavier nuclei fuse with the microscopic model. 19

20 III. Superheavy element synthesis 154 Sm Gd 126X Deep inelastic transfer reaction 20

21 III. Superheavy element synthesis 154 Sm Gd 126X Deep inelastic transfer reaction 21

22 Summary Three-dimensional TDHF with full Skyrme functional and without any symmetry restrictions; The importance of l*s force in heavy-ion collisions; The inclusion of tensor force improve the agreement with experimental cross sections; Quasifission and extra-push in heavy and superheavy elements synthsis; at the ECT*, Trento, Italy, Sep. 1-4,

23 Thank you for your attention Humboldt Kolleg entitled "Interacting Structure and Reaction Dynamics in the Synthesis of the Heaviest Nuclei" 23

24 Effect of spin-orbit force on dissipation dynamics P.-G. Reinhard et. al., Phys. Rev. C 37, 1026 (1988). the difference l*s force symmetry restrictions gradient of density Gao-Feng Dai, Lu Guo, En-Guang Zhao, and Shan-Gui Zhou, Phys. Rev. C90, (2014). at the ECT*, Trento, Italy, Sep. 1-4,

25 Effect of spin-orbit force on dissipation dynamics The time-even coupling of spin-orbit force plays a dominant role at low energies, while the influence of time-odd terms is notable at high energies. 25