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

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

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

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

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

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

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

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

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

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

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

time Period/2 Large mean free path Neutrons of projectile Target neutrons Space period/2 time Period/2 Acceleration (for Ca) Time evolution of center-of-mass velocity time Observation of the early acceleration Velocity [(2/3)* 10 9 m/s] (in lab. frame) Vlasov eq. ( 16 O+ 16 O) Ohnishi-Horiuchi-Wada 1990: via Vlasov eq. ( 16 O+ 16 O) Previous work Dissipative Diabatic Dynamics (Norenberg 1983: large mean free path via Dissipative Diabatic Dynamics) ・・ head-onstable-stable : head-on & stable-stable reaction study → we consider “non head-on” & “non-stable” reaction

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

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

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

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

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

Observation of the early acceleration time time Early acceleration in stable-unstable collision Velocity [(2/3)* 10 9 m/s] Acceleration Acceleration which is found in the motion of lighter nuclei Neutrons of projectile Protons of projectile

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

t = 20.0 projectile P p n n projectile Early state of 4 nucleons in projectile p+p+p+p+ n+n+n+n+ p-p-p-p- n-n-n-n- rather distant correlation Description of projectile 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 t = 13.0 neutron proton (it does not mean weak) Index : sign of Jz y y [fm] x x [fm] neighboring correlation Deuteron neighboring picture (n +, p + ) (n -, p - ) always

4 He + 40 Ca x x [fm] TDHF calculation of non-zero impact parameter Impact parameter = fm Initial energy (E/A = 0.7MeV) 30.8MeV x x [fm] (Almost the radius of 40 Ca) t = 0.0(s) x x [fm] y y [fm] Deuteron neighboring picture Center of mass motion For comparison neutron proton Velocity [(2/3)* 10 9 m/s] time Neutrons of projectile acceleration L-S force dominant small

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

Different contact time for N & P x x [fm] Contact time for N & P is different Estimated contact time = 14.0 dt for N Estimated contact time = 15.5 dt for P Neutron density Proton density dt = 1.5 * s Time () Time (*dt [sec])

Early accelerations are clearly weakened, when time time Velocity [(2/3)* 10 9 m/s] Pauli effect It is mainly due to that Pauli effect is not so effective relative to the case of head-on collision (full overlap case). In this neutron-rich case, Neutrons of projectile Protons of projectile NeutronProton we can say that there is no acceleration for projectile any more !!

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

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

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