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)
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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
TDHF3D-code
size
Bonche-Grammatico-Koonin 1978
Each single particle wave function is defined on
the (31)D lattice
space
time
3D lattice
Unit
Spatial Discretization
?x
?x
?x
Mesh size ?x 0.8 fm
of unit
?t 0.01510-22 s
6
Collision of Ca isotopes
4He
Ca
Neutron
Proton
Reaction
4He Ca ?
7
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 _at_
  projectile

during reaction (especially for neutron-rich
case) ?
P
n
p
n
projectile
9
initial energy
TDHF calculation
30.8MeV
4He 40Ca
(spherical-spherical)
(E/A 0.7MeV)
For comparison
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
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 motion of projectile
12
Observation of the early acceleration
Large mean free path
Velocity (2/3) 109 m/s (in lab. frame)
Space period/2
Acceleration
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.
(16O16O)

(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 12C
4He 16O
velocity
velocity
Neutrons of projectile
Neutrons of projectile
Other neutrons
Other neutrons
time
time
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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
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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
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
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
t 20.0
neutron
(it does not mean weak)
proton
y fm
t 13.0
p-
n-
nucleon _at_ projectile
Index sign of Jz
x fm
Deuteron neighboring picture
(n, p) ------ (n-, p-)
always
No significant difference for t 13.0 to 20.0.
?It is due to the Pauli effect between originally
44 1s-nucleons, than from other nucleons
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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
The same
(Almost the radius of 70Ca)
y fm
t 0.0(s)
x fm
x fm
dt 1.5 10-24s
23
Different contact time for N P
x fm
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
x fm
Brand new different scattering
0
Time (dt sec)
Impact parameter 6.668 fm
dt 1.5 10-24s
10
Center-of-mass motion
y fm
20
30
t 0.0
x fm
40
Di-neutron di-proton neighboring picture
Isospin-difference dominant
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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 _at_ projectile
Index sign of Jz
Di-neutron di-proton picture
x fm
It is due to the Neutron rich effect (?
unbalance between N P)
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Summary

• 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.
Di-neutron di-proton picture
Deuteron 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
bfm
Contactable or not
0