Reaction mechanism in neutron-rich nuclei

1. Reaction mechanism in neutron-rich nuclei Yoritaka Iwata1 and Takaharu Otsuka1,2 1Department of Physics, University of Tokyo 2CNS, University of Tokyo Advices about using TDHF code: C. Simenel (Saclay & MSU) Powered by TKYNT4

2. TDHF formalism (Dirac 1930, Bonche-Koonin-Negele 1976 ～) for nuclear physics Schrodinger equation ・・ Slater determinant antisymmetrizer TDHF equation TDHF Lagrangian (← time-dependent variational principle)

3. TDHF eq. for each single particle wave function From substitution, we obtain TDHF equations for single particle wave function → One body evolution Antisymmetrized potential

4. Skyrme interaction (Skyrme 1956　～) SLy4d SLy4d Chabanat - Bonche - Hansel, 1995

5. size “TDHF3D-code” z y Symmetric about z=0 plain x Bonche-Grammatico-Koonin 1978 ～ Each single particle wave function is defined on the (3+1)D lattice space time 3D lattice Unit Spatial Discretization Δx Δx Δx Mesh size: Δx = 0.8 fm of unit Δt = 0.015×10-22 s

6. Collision of “Ca isotopes” 4He **Ca Neutron Proton Reaction 4He + **Ca →　・・・

7. A spot light is casting on… “Very first few moments of reaction” Relative low energy collision Time 1 4He 1) Initial **Ca The very first few moments 2 2) Contact 3 3) Full overlap

8. View points • Accelerations in early times • Can we see scatterings according to the Pauli effect ? • Is there a specific neighboring for 4 nucleon @ projectile during reaction (especially for neutron-rich case) ? P n p n projectile

9. initial energy TDHF calculation 30.8MeV 4He +40Ca (spherical-spherical) For comparison (E/A = 0.7MeV) Impact parameter = 0.0 fm y [fm] t = 0.0(s) x [fm] dt = 1.5 * 10-24s

10. Time evolution(by TDHF) x [fm] Each single wave 7/2 f 7/2 Neutrons of projectile 1s knock out contact 1/2 1s1/2 f 7/2 7/2 Protons of projectile 1s knock out contact 1s1/2 1/2 Estimated contact time = 10.0 dt |Jz| start to change at 14.0 dt |Jz| becomes larger than 1/2 at 22.0 dt (sufficient to be non 1s-state) |Jz| has maximal at 28.0 dt dt = 1.5 * 10-24s y [fm] 0 10 Contact 20 Composite nuclei 30 40 Time (*dt [sec])

11. What happens in the 1s knock out time ? Center-of-mass 1s knock out t = 22.0 neutron proton y [fm] Highly corresponding t = 14.0 t = 28.0 t = 0.0 contact Copy from the former page nucleon @ projectile t = 22.0 x [fm] Trace of projectile (calculated result) Jz evolution t = 14.0 Estimated contact time = 10.0 dt Scattering Separated (n-p) pairs always have the same sign of nuclear spin. |Jz| start to change at 14.0 dt 1s neutrons @ Ca |Jz| becomes larger than 1/2 at 22.0 dt I.e. (n+, p+) ------ (n-, p-) deuterons (sufficient to be non 1s-state) |Jz| has maximal at 28.0 dt ← Scattering due to the Pauli effect 2 neutrons @ He Center-of-mass motion of projectile

12. Observation of the early acceleration Large mean free path Velocity [(2/3)* 109 m/s] (in lab. frame) Acceleration Space period/2 time Period/2 Neutrons of projectile time Period/2 Space period/2 Target neutrons (for Ca) time Time evolution of center-of-mass velocity Previous work Ohnishi-Horiuchi-Wada 1990: via Vlasov eq. (16O+16O) ・・ (Norenberg 1983: large mean free path via Dissipative Diabatic Dynamics) : head-on & stable-stable reaction study → we consider “non head-on” & “non-stable” reaction

13. Supplement Acceleration can be seen in other targets 4He +16O 4He +12C velocity velocity Neutrons of projectile Neutrons of projectile Other neutrons Other neutrons time time

14. Brief summary for stable-reaction Scattering due to the Pauli effect ~ “Acceleration” They are found in the dynamics of the lighter nuclei 4He 40Ca, 16O , 12C

15. The previous arguments are preparations… Reaction of neutron-rich nuclei 4He +70Ca For the early acceleration, nuclear reaction with unstable nuclei New non zero impact parameter (particular in 3D-space) New

16. TDHF calculation of neutron-rich nuclei 4He +70Ca Initial energy 51.8MeV (E/A = 0.7MeV) Impact parameter = 0.0 fm y [fm] t = 0.0(s) x [fm] dt = 1.5 * 10-24s

17. Different contact time for N & P 7 Neutron density 7 Proton density Estimated contact time = 7.0 dt for N Estimated contact time = 8.0 dt for P Contact time for N & P is different dt = 1.5 * 10-24s x [fm] y [fm] 0 10 Already contacted 20 Composite nuclei 30 Passing through Total density Time (*dt [sec])

18. Observation of the early acceleration Velocity [(2/3)* 109 m/s] Velocity [(2/3)* 109 m/s] Acceleration Acceleration Neutrons of projectile Protons of projectile time time Early acceleration in stable-unstable collision which is found in the motion of lighter nuclei

19. Different scattering for N and P inside “the neutron skin” Center of mass motion = Trace of neutron @ He passing neutron skin neutron y [fm] t = 5.0 ～10.0 proton t = 30.0 t = 0.0 t = 10.0 t = 20.0 magnify x [fm] Trace of nucleon @ He (calculated result) t = 10.0 y [fm] t = 7.0 neutron proton x [fm] neutron skin of Ca target dt = 1.5 * 10-24s x [fm] y [fm] 0 10 Already contacted 20 Composite nuclei 30 Passing through Time (*dt [sec])

20. Early state of 4 nucleons in projectile Description of projectile neighboring correlation P n p+ n+ p n projectile rather distant correlation neutron t = 20.0 (it does not mean weak) proton y [fm] t = 13.0 p- n- nucleon @ projectile Index: sign of Jz x [fm] Deuteron neighboring picture always (n+, p+) ------ (n-, p-) No significant difference for “t = 13.0 to 20.0”. →It is due to the Pauli effect between originally 4+4 1s-nucleons, than from other nucleons

21. TDHF calculation of non-zero impact parameter 4He +40Ca Initial energy 30.8MeV For comparison (E/A = 0.7MeV) Impact parameter =4.518 fm Velocity [(2/3)* 109 m/s] small (Almost the radius of 40Ca) acceleration Neutrons of projectile y [fm] time Center of mass motion y [fm] neutron x [fm] proton t = 0.0(s) Deuteron neighboring picture x [fm] L-S force dominant x [fm]

22. TDHF calculation of neutron-rich nuclei 4He +70Ca Initial energy 51.8MeV (E/A = 0.7MeV) Impact parameter =6.668 fm (Almost the radius of 70Ca) The same y [fm] t = 0.0(s) x [fm] x [fm] dt = 1.5 * 10-24s

23. Different contact time for N & P x [fm] 14 Neutron density 14 Proton density Estimated contact time = 14.0 dt for N Estimated contact time = 15.5 dt for P Contact time for N & P is different 0 Time (*dt [sec]) dt = 1.5 * 10-24s 10 20 30 40

24. Early accelerations are clearly weakened, when In this neutron-rich case, we can say that there is no acceleration for projectile any more !! Velocity [(2/3)* 109 m/s] Velocity [(2/3)* 109 m/s] Neutron Proton Neutrons of projectile Protons of projectile time time It is mainly due to that Pauli effect is not so effective relative to the case of head-on collision (full overlap case).

25. “Brand new” different scattering x [fm] Neutron skin t = 24.0 t = 30.0 t = 35.0 neutron proton 0 Time (*dt [sec]) Impact parameter =6.668 fm dt = 1.5 * 10-24s Center-of-mass motion 10 y [fm] 20 30 t = 0.0 x [fm] 40 Di-neutron & di-proton neighboring picture Isospin-difference dominant

26. Early state of 4 nucleons in projectile Description of projectile P n neighboring correlation p n projectile p+ n+ neutron p- n- proton y [fm] t = 24.0 t = 30.0 rather distant correlation nucleon @ projectile Index: sign of Jz Di-neutron & di-proton picture x [fm] It is due to the Neutron rich effect (← unbalance between N& P)

27. Summary neutron proton • Relative large early accelerations are seen mainly in head-on collisions. → Large acceleration is due to the Pauli effect (with full overlap) • Impact parameter and neutron-richness dependence can be seen in the neighboring property of projected 4 nucleons. Deuteron picture Di-neutron & di-proton picture Frequently found states of projectile in the very early time nn/ nz ( = neutron richness of target ) 4 nucleons of projectile Near the “drip line” Di-neutron & di-proton picture Deuteron picture Pauli scattering small acceleration (large acceleration) Single center Deuteron picture “stable line” b[fm] Contactable or not 0