时间相关密度泛函理论的发展 及其在重离子碰撞中的应用

Transcription

1 时间相关密度泛函理论的发展 及其在重离子碰撞中的应用 郭璐 中国科学院大学 第十七届全国核结构大会, 辽宁师范大学,2018 年 7 月 9 日 1

2 Contents I. Introduction of TDHF approach II. Development of theoretical approach spin-orbit force tensor force density-constraint TDHF particle number projection III. Applications of theoretical approach heavy-ion interaction potential and sub-barrier fusion multi-nucleon transfer reaction quasifission dynamics IV. Summary and perspectives 2

3 Time-dependent Hartree-Fock theory Time-dependent Hartree-Fock (TDHF) theory t, 2 S = ( t) H i ( t) dt H = t + v t1 t i ij i= 1 i j A A E f 1 (r 1, r2,, ra, t) = det ( ri, t), i = h A! t Advantages: Fully microscopic, parameter-free theory in heavy-ion collisions; Nuclear structure and reactions in a unified framework (same EDF); Dynamical and quantum effects are automatically incorporated; Limitations: Quantum tunneling is missing; 3

4 TDHF theory: historical remarks TDHF was first applied to nuclear physics in 1976 fusion dynamics Deep inelastic collisions fission dynamics Resonances dynamics nuclear molecular collective excitation giant resonance = RPA fusion deep inelastic collisions 4

5 TDHF theory: historical remarks After the first application, many extensive studies in 70s and 80s many approximations and restrictions on effective interaction Omission of spin-orbit force symmetries Axial-symmetry 2D restriction Boneche et al., PRC17, 1700 (1978) Maruhn et al., PRC31, 1289 (1985) Davies et al., PRC 23, (1981) Reinhard et al. PRC37, 1026 (1988) A hindrance for the theoretical development 5

6 TDHF theory: historical remarks 6

7 TDHF theory: historical remarks 7

8 TDHF theory: historical remarks Puzzle of small fusion window The conflict between TDHF prediction and experimental data promotes the theoretical development. 8

9 TDHF theory: historical remarks Inclusion of time-even spin-orbit force A. S. Umar et al., PRL56, 2793 (1986) 9

10 TDHF theory: historical remarks Inclusion of time-even spin-orbit force A. S. Umar et al., PRL56, 2793 (1986) Upper fusion threshhold was increased more than 2 times with l*s; Energy dissipation was increased significantly with l*s; 10

11 TDHF theory: historical remarks Inclusion of time-even spin-orbit force A. S. Umar et al., PRL56, 2793 (1986) Upper fusion threshhold was increased more than 2 times with l*s; Energy dissipation was increased significantly with l*s; solved the puzzle of small fusion window 11

12 Importance of spin-orbit force Galilean invariance in TDHF effective interaction inclusion of both time-even and time-odd spin-orbit force 12

13 Importance of spin-orbit force Galilean invariance in TDHF effective interaction inclusion of both time-even and time-odd spin-orbit force symmetries without any symmetry restrictions in 3D coordinate space 13

14 Importance of spin-orbit force Galilean invariance in TDHF effective interaction inclusion of both time-even and time-odd spin-orbit force symmetries without any symmetry restrictions in 3D coordinate space Time-even l*s is important in low energy, while time-odd l*s is at high energy; Around 40%~65% of the energy dissipation arise from spin-orbit force; G. F. Dai, Lu Guo, E.G. Zhao, and S.G. Zhou, Phys. Rev. C90, (2014) 14

15 Role of tensor force in fusion dynamics TDHF approach effective interaction inclusion of both time-even and time-odd spin-orbit force symmetries without any symmetry restrictions in 3D coordinate space 15

16 Role of tensor force in fusion dynamics TDHF approach effective interaction inclusion of both time-even and time-odd spin-orbit force symmetries without any symmetry restrictions in 3D coordinate space Q: Is there important component of the basic theory that have not yet been implemented? 16

17 Role of tensor force in fusion dynamics TDHF approach effective interaction inclusion of both time-even and time-odd spin-orbit force symmetries without any symmetry restrictions in 3D coordinate space Q: Is there important component of the basic theory that have not yet been implemented? A: tensor force, most obviously missing in HIC 17

18 Role of tensor force in fusion dynamics TDHF approach effective interaction inclusion of both time-even and time-odd spin-orbit force symmetries without any symmetry restrictions in 3D coordinate space Q: Is there important component of the basic theory that have not yet been implemented? A: tensor force, most obviously missing in HIC Tensor force in original Skyrme interaction: 18

19 Role of tensor force in fusion dynamics Energy density functional (EDF) of tensor force Both time-even and time-odd EDF have been included where is the simplified functional used in Sky3D code and most TDHF calculations. 19

20 Role of tensor force in fusion dynamics Energy density functional (EDF) of tensor force Both time-even and time-odd EDF have been included where is the simplified functional used in Sky3D code and most TDHF calculations. the role of tensor force in fusion dynamics (first study) all are doubly magic closed shells---no pairing necessary N s is the total number of spin-unsaturated magic number spin-saturated closed shells: 20, 40 Lu Guo, C. Simenel, L. Shi, C. Yu, Phys. Lett. B (in press) 5 representative collisions N s Reaction 0 40 Ca+ 40 Ca 1 40 Ca+ 48 Ca 2 48 Ca+ 48 Ca 3 48 Ca+ 56 Ni 4 56 Ni+ 56 Ni 20

21 Role of tensor force in fusion dynamics the effects induced by tensor force Difference of fusion barrier with tensor (SLy5t) and without tensor (SLy5) Lu Guo, C. Simenel, L. Shi, C. Yu, Phys. Lett. B (in press) 21

22 Role of tensor force in fusion dynamics the effects induced by tensor force Difference of fusion barrier with tensor (SLy5t) and without tensor (SLy5) What s the origin of these effects? static origin (modification of ground-state density) Lu Guo, C. Simenel, L. Shi, C. Yu, Phys. Lett. B (in press) dynamic origin (vibration, nucleon transfer, dissipation) 22

23 Role of tensor force in fusion dynamics the effects induced by tensor force Difference of fusion barrier with tensor (SLy5t) and without tensor (SLy5) What s the origin of these effects? static origin: frozen Hartree-Fock (FHF) static origin (modification of ground-state density) the importance of dynamical effects which can remarkably modify the barrier Lu Guo, C. Simenel, L. Shi, C. Yu, Phys. Lett. B (in press) dynamic origin (vibration, nucleon transfer, dissipation) 23

24 Role of tensor force in fusion dynamics dynamical origin couplings to intrinsic degrees of freedom, e.g., low-lying vibration; nucleon transfer; dynamical dissipation; 2 1+ state Taking 48 Ca+ 48 Ca as an example: Tensor force shifts 2 + and 3 - states to higher energies; Fusion is dynamically hindered by tensor force; E(SLy5) E(SLy5t) Expt state Lu Guo, C. Simenel, L. Shi, C. Yu, Phys. Lett. B (in press) 24

25 Role of tensor force in fusion dynamics dynamical origin couplings to intrinsic degrees of freedom, e.g., low-lying vibration; nucleon transfer; dynamical dissipation; Taking 48 Ca+ 48 Ca as an example: Tensor force shifts 2 + and 3 - states to higher energies; Fusion is dynamically hindered by tensor force; Fusion dynamics is dominated by low-lying vibrations in symmetric reactions E(SLy5) E(SLy5t) Expt Lu Guo, C. Simenel, L. Shi, C. Yu, Phys. Lett. B (in press) 25

26 Role of tensor force in fusion dynamics dynamical origin couplings to intrinsic degrees of freedom, e.g., low-lying vibration; nucleon transfer; dynamical dissipation; N(SLy5) N(SLy5t) neutron proton Ca proton neutron 56 Ni Taking 48 Ca+ 56 Ni as an example: The competition between vibration and nucleon transfer; The increase of vibration energy increase the dynamical barrier; Large neutron transfer decreases the dynamical barrier; Nucleon transfer is dominant; Lu Guo, C. Simenel, L. Shi, C. Yu, Phys. Lett. B (in press) 26

27 Role of tensor force in fusion dynamics Another important experimental observable Parameter-free calculation Deviation from experiments: P s = ( TDHF exp ) exp 48 Ca+ 48 Ca the theoretical cross section overall overestimates the experiments. Lu Guo, C. Simenel, L. Shi, C. Yu, Phys. Lett. B (in press) 27

28 Role of tensor force in fusion dynamics Another important experimental observable Parameter-free calculation Deviation from experiments: P s = ( TDHF exp ) exp 48 Ca+ 48 Ca with tensor force, the deviation decreases from 1.6 to 0.2 at Coulomb barrier; it improves the agreement dramatically; Lu Guo, C. Simenel, L. Shi, C. Yu, Phys. Lett. B (in press) 28

29 Contents I. Introduction of TDHF approach II. Development of theoretical approach spin-orbit force tensor force density-constraint TDHF particle number projection III. Applications of theoretical approach heavy-ion interaction potential and sub-barrier fusion multi-nucleon transfer reaction quasifission dynamics IV. Summary and perspectives 29

30 Heavy-ion interaction potential and sub-barrier fusion construction of density-constrained TDHF (DC-TDHF) sub-barrier fusion dynamics ρ TDHF (r,t) E*(R(t)) Quasi-Static Energy Surface H - 3 d r ( r) ( r) = 0 DC DC Density constraint method was developed in the mid 1980s; R. Y. Cusson et al., Z. Phys. A 320, 475 (1985); It was first applied to TDHF in 2006, A. S. Umar, V. E. Oberacker, Phys. Rev. C 74, (R) (2006); Afterwards, many applications, A. S. Umar et al., Phys. Rev. 80, (R) (2009), X. Jiang, J. A. Maruhn, S. W. Yan, Phys. Rev. C90, (2014) Advantage: E ( R) = H DC DC DC V ( R) = E ( R) E ( R) E ( R) DC A1 A2 No adjustable parameters---predictive power; There is no need to introduce external constraining operators; the dynamical analog to the static adiabatic approximation 30

31 Heavy-ion interaction potential and subbarrier fusion role of tensor force in heavy-ion interaction potential Lu Guo, A. S. Umar, K. Godbey, Phy. Rev. C (submitted) 31

32 Heavy-ion interaction potential and subbarrier fusion role of tensor force on subbarrier fusion the two-body Schrodinger equation to obtain the penetration factor T L (E) using the incoming wave boundary condition (IWBC) method The fusion cross section above and below the barrier energies: SLy5 SLy5t 32

33 Contents I. Introduction of TDHF approach II. Development of theoretical approach spin-orbit force tensor force density-constraint TDHF particle number projection III. Applications of theoretical approach heavy-ion interaction potential and sub-barrier fusion multi-nucleon transfer reaction quasifission dynamics IV. Summary and perspectives 33

34 Multi-nucleon transfer reaction New isotopes production via multi-nucleon transfer reaction DUBNA Argone KEK GSI

35 Multi-nucleon transfer reaction TDHF studies of multi-nucleon transfer reaction TDHF gives the average number of transferred nucleons for all reaction channels How to obtain the transferred nucleon number for each reaction channel?

36 Multi-nucleon transfer reaction TDHF studies of multi-nucleon transfer reaction TDHF gives the average number of transferred nucleons for all reaction channels How to obtain the transferred nucleon number for each reaction channel? particle number projection method (PNP) particle number projection operator: 1 2 ˆ Pˆ transfer cross sction of primary products: (TDHF+PNP) transfer probability for each channel: = = ˆ i( n N VP ) n d e Pn Pn 2 0 cut ( ) 2 N Z (, ) bmin N, Z, b E = bp b E db C. Simenel, Phys. Rev. Lett. 105, (2010)

37 Multi-nucleon transfer reaction TDHF studies of multi-nucleon transfer reaction TDHF gives the average number of transferred nucleons for all reaction channels How to obtain the transferred nucleon number for each reaction channel? particle number projection method (PNP) particle number projection operator: 1 2 ˆ Pˆ transfer cross sction of primary products: (TDHF+PNP) Statistical decay method (Gemini++) direct comparison with experimental measurement * P P P ( E, J, N, Z; N, Z ) transfer cross sction of primary products: (TDHF+PNP+Gemini) transfer probability for each channel: = = ˆ i( n N VP ) n d e Pn Pn 2 = 0 N, Z N, Z decay N, Z N, Z N N Z Z cut ( ) 2 N Z (, ) bmin N, Z, b E = bp b E db C. Simenel, Phys. Rev. Lett. 105, (2010) cut ( E) 2 bpn Z ( b, ) bmin = N, Z, b E db

38 TDHF studies of multi-nucleon transfer reaction Z. J. Wu, Lu Guo, Phy. Rev. C (to be submitted)

39 TDHF studies of multi-nucleon transfer reaction 58 Ni+ 124 Sn primary products TDHF+PNP secondary products TDHF+PNP+GEMINI Z. J. Wu, Lu Guo, Phy. Rev. C (to be submitted)

40 TDHF studies of multi-nucleon transfer reaction 58 Ni+ 124 Sn primary products TDHF+PNP ongoing project: 238 U+ 248 Cm 58 Ni+ 232 Th secondary products TDHF+PNP+GEMINI 详见 7 月 11 日上午吴振基同学报告 (5 楼 3 号厅 ) Z. J. Wu, Lu Guo, Phy. Rev. C (to be submitted)

41 Contents I. Introduction of TDHF approach II. Development of theoretical approach spin-orbit force tensor force density-constraint TDHF particle number projection III. Applications of theoretical approach heavy-ion interaction potential and sub-barrier fusion multi-nucleon transfer reaction quasifission dynamics IV. Summary and perspectives 41

42 Experimental Synthesis of SHE 114

43 Experimental Synthesis of SHE

44 Experimental Synthesis of SHE 114 Zagrebaev et al., PRC85,014608(2012); Adamian et al., PRC69,014607(2004);

45 TDHF studies of fusion and quasifission 48 Ca+ 244 Pu with E cm = MeV, b=2.0 fm Lu Guo, C. Yu, Z. J. Wu, C. W. Shen, Phys. Rev. C (to be submitted) 45

46 TDHF studies of fusion and quasifission 48 Ca+ 239 Pu 48 Ca+ 244 Pu (1) Collisions with the tip of 239 Pu produce quasifission fragments, while collisions with the side result in fusion; (2) contact time decreases as b; (3) tip: 32Ge+ 82 Pb side: 40Zr+ 74 W; (4) The interplay between quantum shell effect and orientation of deformed nuclei; Lu Guo, C. Yu, Z. J. Wu, C. W. Shen, Phys. Rev. C (to be submitted)

47 TDHF studies of fusion and quasifission 48 Ca+ 239 Pu 48 Ca+ 244 Pu The collision 48 Ca+ 239 Puis much easier to happen quasifission than 48 Ca+ 244 Pu (experiment), More neutron-rich target nucleus will be helpful in the production of SHE(ANU experiments); P CN =σ fus /σ cap, P CN =0.22( 48 Ca+ 244 Pu), P CN =0.14 ( 48 Ca+ 239 Pu)---side (first microscopic P CN ); Lu Guo, C. Yu, Z. J. Wu, C. W. Shen, Phys. Rev. C (to be submitted)

48 TDHF studies of fusion and quasifission Mass-angle distribution: directly measured by experiments = in + TDHF + out Lu Guo, C. Yu, Z. J. Wu, C. W. Shen, Phys. Rev. C (to be submitted)

49 TDHF studies of fusion and quasifission Mass-kinetic distribution: directly measured by experiments Systematic agreement with the Viola formula; Quasifission dynamics is a fully damped motion; Lu Guo, C. Yu, Z. J. Wu, C. W. Shen, Phys. Rev. C (to be submitted)

50 Summary and perspectives Development of theoretical models spin-orbit force tensor force density-constraint TDHF particle number projection 50

51 Summary and perspectives Development of theoretical models spin-orbit force tensor force density-constraint TDHF particle number projection Applications of TDHF in heavy-ion collisions heavy-ion interaction potential and sub-barrier fusion multi-nucleon transfer reaction quasifission dynamics 51

52 Summary and perspectives Development of theoretical models spin-orbit force tensor force density-constraint TDHF particle number projection Applications of TDHF in heavy-ion collisions heavy-ion interaction potential and sub-barrier fusion multi-nucleon transfer reaction quasifission dynamics Perspectives basis space, especially with pairing (TDHFB, TDHF+BCS) beyond the independent-particle approximation (TDRPA) spontaneous fission and induced fission the role of two-body collisions 52

53 Summary and perspectives Development of theoretical models spin-orbit force tensor force density-constraint TDHF particle number projection Applications of TDHF in heavy-ion collisions heavy-ion interaction potential and sub-barrier fusion multi-nucleon transfer reaction quasifission dynamics Perspectives basis space, especially with pairing (TDHFB, TDHF+BCS) beyond the independent-particle approximation (TDRPA) spontaneous fission and induced fission the role of two-body collisions Thanks for your attention! 53