Macroscopic properties in low-energy nuclear reactions by microscopic TDDFT

Transcription

1 Macroscopic properties in low-energy nuclear reactions by microscopic TDDFT Kouhei Washiyama (RIKEN, Nishina Center, Japan) Collaboration with Denis Lacroix (GANIL), Sakir Ayik (Tennesse Tech.) Key word: fusion, TDDFT(TDHF), nucleus-nucleus potential, energy dissipation, fusion hindrance Quantitative Large Amplitude Shape Dynamics: fission and heavy ion fusion Oct. INT, Seattle

2 Nucleus-nucleus potential Low-energy nuclear reactions E/A < 10 MeV 16 O Sm V B r B Woods-Saxon Proximity Double-folding Coupled-channels method Dasgupta et al., Ann. Rev. Nuc. Par. Sci. (1998) Balantekin, Takigawa, Rev. Mod. Phys. (1998) Hagino, Takigawa, PTP (2012) r [fm]

3 Macroscopic, Microscopic picture Macroscopic Microscopic R Collective degrees of freedom Single-particle degrees of freedom Potential: V(R) Energy dissipation Aim Study the property of macroscopic quantities by TDHF

4 Time-dependent Hartree-Fock (TDHF) h: self-consistent single-particle Hamiltonian (static case ) Self-consistent description for both static and Bonche et al., PRC 13 (1976) Flocard et al., PRC 17 (1978) Kim et al., J. Phys. G 23 (1997) Simenel et al., PRL 86 (2001) Nakatsukasa, Yabana, PRC 71 (2005) Umar, Oberacker, PRC 73 (2006) Maruhn et al., PRC 74 (2006) dynamical properties Single-particle: Quantum, Collective motion: Classical Low energy: mean-field approximation 3D-TDHF code by P. Bonche (Kim, Otsuka, Bonche, J. Phys. G23(1997)1267) Input: Skyrme SLy4d parameterization 3D, dx = 0.8 fm, dt = 0.45 fm/c

5 Energy density functional Skyrme energy density functional Bender, Heenen, Reinhard, Rev. Mod. Phys. 75 (2003) 121

6 Numerical method for solving TDHF

7 Recent applications of TDHF Density-constrained TDHF Umar, Oberacker, PRC74(2006) U U central collision Golabek, Simenel, PRL103(2009) Charge equilibration Iwata et al., PRL104 (2010) Transfer reaction Sekizawa, Yabana, PRC88(2013)014614

8 Frozen density approximation: Sudden Denisov, Norenberg, EPJA15(2002)375 R Approximate that densities are frozen to be their ground state densities during time evolution R

9 Density-constrained TDHF: Adiabatic with minimization Umar, Oberacker, PRC74(2006) R Energy is obtained by minimization with a constraint on the density from TDHF time evolution R

10 Method: Extract potential and dissipation X Washiyama, Lacroix, PRC78 (2008) Central collisions Mass time 3. R R: Relative distance P: Momentum V: Potential g : Friction coefficient

11 Method: Extract potential and dissipation X Washiyama, Lacroix, PRC78 (2008) Central collisions Mass time 3. Two trajectories (R 1, P 1 ), (R 2, P 2 ) at slightly different energies (E 1, E 2 ) R

12 Result: Comparison of potentials Washiyama, Lacroix, PRC78 (2008) O + 16 O Agree with each model Validation of our model

13 Energy dependence of potential Washiyama, Lacroix, PRC78 (2008) Ca + 40 Ca High E cm = Frozen density

14 Energy dependence of potential Washiyama, Lacroix, PRC78 (2008) Ca + 40 Ca High E cm = Frozen density Decrease of the barrier: from high E cm to low E cm

15 Energy dependence of potential Washiyama, Lacroix, PRC78 (2008) Density distribution E cm =55MeV E cm =90MeV

16 Systematics of potentials High E cm TDHF Low E cm TDHF 16 O + 40 Ca 40,48 Ca + 40,48 Ca 16 O Pb 40 Ca + 96 Zr

17 Energy dependence of friction coefficient g: friction coefficient E cm = P 2 /2μ + V + E dissipation

18 Energy dependence of friction coefficient g: friction coefficient Friction E cm = P 2 /2μ + V + E dissipation Washiyama, Lacroix, Ayik, PRC79(2009)024609

19 Energy dependence of friction coefficient g: friction coefficient E cm = P 2 /2μ + V + E dissipation Friction Density distribution E cm =55MeV E cm =90MeV Washiyama, Lacroix, Ayik, PRC79(2009)024609

20 Energy dependence of friction coefficient g: friction coefficient E cm = P 2 /2μ + V + E dissipation Friction Density distribution E cm =55MeV E cm =90MeV Washiyama, Lacroix, Ayik, PRC79(2009)024609

21 y (fm) How about heavy systems? Heavy: Charge product > Sn + 96 Zr, E cm = 228 MeV, Charge product = 50 x 40 = 2000 X (fm) (fm -3 )

22 y (fm) How about heavy systems? Heavy: Charge product > Sn + 96 Zr, E cm = 228 MeV, Charge product = 50 x 40 = 2000 X (fm) (fm -3 )

23 Fusion hindrance in heavy systems Fusion probability decreases in Z P Z T > 1600 systems C.-C. Sahm et al., NPA441 (1985) Zr Sn 220 Th 40 Ar Hf 220 Th Extra push energy Potential model

24 Fusion hindrance in heavy systems Compound nucleus 40 Ar Hf 220 Th 96 Zr Sn 220 Th Quasi-fission Analysis with Langevin equation Aritomo et al., PRC85 (2012)

25 Fusion threshold energy from TDHF E thres - V FD [MeV] Simenel et al., J.Phys.Conf.Ser. 420 (2013) Guo, Nakatsukasa, EPJ.Conf. 38 (2012) 09003

26 Results: Comparison of potentials Heavy system vs. Light system Z P Z T = 2000 Z P Z T = 400

27 Results: Comparison of potentials Heavy system vs. Light system Z P Z T = 2000 Z P Z T = 400 Vanish the potential barrier Energy dependence is less around the barrier

28 Results: Comparison of potentials Our model v.s. Density-constrained TDHF Oberacker et al., PRC 82 (2010)

29 Potentials of heavy systems Z P Z T = 1640 Z P Z T = 2000 Z P Z T = 2160 Z P Z T = 2460

30 Property of friction Heavy system vs. Light system Same order of magnitude Energy dependence is less

31 Dissipation energy Heavy system vs. Light system Same order of magnitude

32 Origin of fusion hindrance? Potential Dissipated energy ΔV = 7.7MeV 3.7MeV E thres V FD = = 14 MeV ΔV + E diss = = 11.4 MeV at R stop A part of the origin comes from more inside of the barrier

33 Summary Macroscopic reduction from TDHF in low-energy reactions Nucleus-nucleus potential and energy dissipation are extracted Energy dependence Fusion hindrance Change the property of the barrier