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Gogny-TDHFB calculation of nonlinear vibrations in 44,52 Ti

Gogny-TDHFB calculation of nonlinear vibrations in 44,52 Ti. Yukio Hashimoto Graduate school of pure and applied sciences, University of Tsukuba. Introduction TDHFB equation Linear region 4-1. Nonlinear region (vibration type) 4-2. Nonlinear region (relaxation type)

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Gogny-TDHFB calculation of nonlinear vibrations in 44,52 Ti

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  1. Gogny-TDHFB calculation of nonlinear vibrations in 44,52 Ti Yukio Hashimoto Graduate school of pure and applied sciences, University of Tsukuba • Introduction • TDHFB equation • Linear region • 4-1. Nonlinear region (vibration type) • 4-2. Nonlinear region (relaxation type) • 5. summary

  2. 1. Introduction ☆ random phase approximation (RPA) on a large scale T. Inakura, from “Report of KEK Ohgata Simulation Program (2010)” ☆ S. Ebata et al., Phys. Rev. C 82 (2010), 034306. “canonical-basis TDHFB” with Skyrme force ☆ in this talk, Gogny force is used in TDHFB calculations Gogny force: ph channel  pp channel role of pairing correlation in vibration / relaxation

  3. 2. TDHFB equation

  4. Equations of motion of matrices U & V see Ring & Schuck

  5. Gogny-D1S Gauss part density dependent part L-S part Coulomb part is NOT included ・basis function:three-dimensional harmonic oscillator wave functions ・space:

  6. initial conditions:  ・Q20 type impulse on ground state(impulse type)  ・constrained state with quadrupole operator(constraint type) initial U & V HFB ground state U, V Q0:matrix representation of multipole operator

  7. Energy conservation tdhf

  8. 3. Linear region

  9. Example:20O quadrupole oscillation (small amplitude)

  10. * 18– 22O quadrupole mode * 34 – 38Mg quadrupole (K=0) mode * 44,50,52,54Ti quadrupole mode

  11. 4-1.Nonlinear region(oscillation type)

  12. quadrupole oscillation and pairing52Ti pairing is zero oblate prolate

  13. initial conditions HF “pocket”

  14. 52Ti

  15. U V ( ) k k definition occupation probability in orbital(k) :HFB matrix α:numerical basis label

  16. initial condition: Q20 = 0 fm^2 (impulse) initial condition: Q20 = 140 fm^2 (constraint)

  17. initial condition: Q20 = 140 fm^2 initial condition: Q20 = - 165 fm^2 initial condition: Q20 = 0 fm^2 (impulse) initial condition: Q20 = 140 fm^2

  18. 44Ti vibration ( f7/2 members in initial stage) single-particle energies vs Q20 time (fm) Fermi energy 0 100 200 quadrupole moment (fm^2)

  19. ( f7/2 members in initial stage) single-particle energies vs Q20 time (fm) 0 100 200 quadrupole moment (fm^2)

  20. occupation probability p(k) (protons) HFB eigen energies (MeV) HFB energies (MeV) Time (fm)

  21. 4-2. Nonlinear region(relaxation type)

  22. occupation probabilities p(k) ( neutron, minus parity) 44Ti Energy vs Q20 Energy (MeV) 2 Q20 (fm ) 4000 0 2000 Time (fm)

  23. relaxation of quadrupole oscillation( 44Ti ) 2 fm occupation probability p(k) (protons) time (fm) Fermi energy occupation probability p(k) single particle energy (MeV) time(fm) quadrupole moment

  24. relaxation of quadrupole oscillation( 44Ti ) occupation probability p(k) (protons) time (fm) occupation probability p(k) single particle energy (MeV) time(fm) quadrupole moment 2 fm

  25. summary (small amplitude case) RPA linear response  strength functions 2. (nonlinear case) i) long period oscillation accompanied with “adiabatic” configuration around single-particle level crossing region ii) relaxation together with adiabatic configuration across single-particle level crossing

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