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![Page 1: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/1.jpg)
Yoritaka IwataYoritaka Iwata11 and Takaharu Otsuka and Takaharu Otsuka1,21,2
Reaction mechanism Reaction mechanism in neutron-rich nucleiin neutron-rich nuclei
11Department of Physics, University of TokyoDepartment of Physics, University of Tokyo
Advices about using TDHF code: C. Simenel (Saclay & MSU)Advices about using TDHF code: C. Simenel (Saclay & MSU)
22CNS, University of TokyoCNS, University of Tokyo
Powered by TKYNT4Powered by TKYNT4
![Page 2: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/2.jpg)
Schrodinger equationSchrodinger equation
)],(),(),([)(| 211 trtrtrAt nnn
)(|)(| tHti t
Vm
HN
jj
j
1
22
2
Slater determinantSlater determinant
0 Hidt t
TDHF TDHF equationequation
・・・・
TDHF LagrangianTDHF Lagrangian
TDHF formalismTDHF formalism
(← time-dependent variational principle)(← time-dependent variational principle)
antisymmetrizerantisymmetrizer
(Dirac 1930, Bonche-Koonin-Negele 1976 ~ )for nuclear physicsfor nuclear physics
![Page 3: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/3.jpg)
TDHF eq. TDHF eq. for each single particle wave functionfor each single particle wave function
'),'(),',(2
22
drtrtrrVm
i iij
it
j
jj drdrtrtrrrrrVtrrV '''''),'''(),''()''',','',(~
),',( * Antisymmetrized potential
TDHF equations for single particle wave TDHF equations for single particle wave functionfunction
From substitution, we obtainFrom substitution, we obtain
→ → One body evolutionOne body evolution
![Page 4: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/4.jpg)
Skyrme Skyrme interactioninteraction
ji
ijkji
ij vvV )3()2(
)()1( 2100 rrPxt
)')()(()1(2
1 22121
211 krrrrkPxt
')()1( 2122 krrkPxt
')()( 21210 krrkiW
SLy4SLy4dd
SLy4dSLy4d Chabanat - Bonche - Hansel, 1995
(Skyrme 1956 ~ )
![Page 5: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/5.jpg)
size
x
y
z
3D 3D lattice lattice
Each single particle wave functionsingle particle wave function is defined on the (3+1)D lattice
Mesh size: Δx = 0.8 fm
Symmetric about z=0 plain
Spatial DiscretizationSpatial Discretization
ΔxΔx
Δx
““TDHF3D-TDHF3D-code”code”
Bonche-Grammatico-Koonin 1978 ~
spacspacee
timetime
Δt = 0.015×10-22 s
UnitUnit
of unit
![Page 6: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/6.jpg)
Collision of “Collision of “Ca isotopesCa isotopes””
4He + **Ca → ・・・
Neutron
Proton
4He
**Ca
ReactionReaction
![Page 7: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/7.jpg)
““Very first few moments of Very first few moments of reactionreaction””
A spot light is casting on…A spot light is casting on…
4He **Ca
1) Initial1) Initial
2) Contact2) Contact
3) Full overlap3) Full overlap
Relative low energy collisionRelative low energy collision
The very first The very first few moments few moments
11
22
33
TimeTime
![Page 8: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/8.jpg)
View pointsView points
Can we see scatterings according to the Pauli effect ?Can we see scatterings according to the Pauli effect ?
Is there a specific neighboring for 4 nucleon @ Is there a specific neighboring for 4 nucleon @ projectileprojectile
Accelerations in early timesAccelerations in early times
PP
pp
nn
nn projectileprojectile
during reaction (especially for neutron-rich during reaction (especially for neutron-rich case) ?case) ?
![Page 9: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/9.jpg)
(spherical-spherical)(spherical-spherical)
4He +40Ca
tt = = 0.0(s)0.0(s)
initial energy30.8MeV
(E/A = 0.7MeV)
yy [fm]
xx [fm]
dt = 1.5 * 10-24s
Impact parameter = 0.0 fmImpact parameter = 0.0 fm
TDHF calculationTDHF calculation
For comparisonFor comparison
![Page 10: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/10.jpg)
0 ||Jz
1/21/2
1/21/2
Estimated contact time = Estimated contact time = 10.0 10.0 dtdt
|Jz| start to change at |Jz| start to change at 14.0 14.0 dtdt
Protons of Protons of projectileprojectile
Neutrons of Neutrons of projectileprojectile
|Jz| becomes larger than 1/2 at |Jz| becomes larger than 1/2 at 22.0 22.0 dtdt
(sufficient to be non 1s-state)(sufficient to be non 1s-state)
7/27/2
7/27/2
|Jz| has maximal at |Jz| has maximal at 28.0 28.0 dtdt
1s1s1/21/2
1s1s1/21/2
f f 7/27/2
f f 7/27/2
1s knock out1s knock out
1s knock out1s knock out
contactcontact
contactcontact
)(||)( tt ii Jz Each single waveEach single wave
Time evolution(by TDHF)Time evolution(by TDHF)
20
10
0
30
40
ContactContact
Composite nucleiComposite nuclei
xx [fm]yy [fm]
Time (Time (*dt [sec]))
dt = 1.5 * 10-24s
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What happens in the What happens in the 1s knock out time ?1s knock out time ?
jj
jii xxx )(ˆ 2
)ˆ,ˆ( ii yxj
jjii yyy )(ˆ 2
Center-of-massCenter-of-mass
Trace of projectile (calculated result)Trace of projectile (calculated result)
t t = 0.0= 0.0
t t = 14.0= 14.0
t t = 22.0= 22.0
t t = 22.0= 22.0
t t = 28.0= 28.0contactcontact
yy [f
m]
xx [fm]
Estimated contact time = Estimated contact time = 10.0 10.0 dtdt
|Jz| start to change at |Jz| start to change at 14.0 14.0 dtdt
(sufficient to be non 1s-state)(sufficient to be non 1s-state)
|Jz| has maximal at |Jz| has maximal at 28.0 28.0 dtdt
|Jz| becomes larger than 1/2 at |Jz| becomes larger than 1/2 at 22.0 22.0 dtdt
Jz evolutionJz evolution
t t = 14.0= 14.0ScatteringScattering
2 neutrons @ He2 neutrons @ He← Scattering due to the Pauli effectPauli effect
Copy from the former Copy from the former pagepage
Highly correspondingHighly corresponding
1s neutrons @ Ca1s neutrons @ Ca
1s knock out1s knock outneutronneutronprotonproton
nucleon @ projectilenucleon @ projectile
Separated (n-p) pairs Separated (n-p) pairs alwaysalways have the same sign have the same sign of nuclear spin.of nuclear spin.
I.e. (nI.e. (n++, p, p++) ------ (n) ------ (n--, p, p--)) deuteronsdeuterons
Center-of-mass motion of projectileCenter-of-mass motion of projectile
![Page 12: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/12.jpg)
time time Period/2Period/2
Large mean free Large mean free pathpath
Neutrons of projectile
Target neutrons
Space Space period/2period/2
Space period/2Space period/2
time time Period/2Period/2
AcceleratioAccelerationn
(for Ca)(for Ca)
Time evolution of center-of-mass Time evolution of center-of-mass velocityvelocity
timetime
Observation of the Observation of the early accelerationearly acceleration
Velocity [(2/3)* 10Velocity [(2/3)* 1099 m/s] (in lab. frame) m/s] (in lab. frame)
Ohnishi-Horiuchi-Wada 1990: via Vlasov eq. (Vlasov eq. (1616O+O+1616O)O)Previous workPrevious work
(Norenberg 1983: large mean free path via Dissipative Diabatic DynamicsDissipative Diabatic Dynamics)・・
: head-onhead-on & stable-stablestable-stable reaction study→ → we consider “we consider “non head-on”non head-on” & “ & “non-stable”non-stable” reaction reaction
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4He +12C
4He +16O
Neutrons of projectileNeutrons of projectile
velocityvelocity
timetime timetime
velocityvelocity
Neutrons of projectileNeutrons of projectile
Acceleration can be seen in other targets Acceleration can be seen in other targets
Other neutronsOther neutrons Other neutronsOther neutrons
SupplementSupplement
![Page 14: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/14.jpg)
Scattering Scattering due todue to the Pauli effect the Pauli effect
They are found in the dynamics of the lighter the lighter nucleinuclei
40Ca, 16O , 12C
4He
““Acceleration”Acceleration”
~~
Brief summary for stable-reactionBrief summary for stable-reaction
![Page 15: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/15.jpg)
Reaction of neutron-rich Reaction of neutron-rich nucleinuclei
The previous arguments are preparations…
4He +70Ca
NeNeww
For the early acceleration,
nuclear reaction with unstable nuclei
NeNeww
non zero impact parameter (particular in 3D-space)
![Page 16: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/16.jpg)
4He +70Ca
tt = = 0.0(s)0.0(s)
Initial energy
(E/A = 0.7MeV)
yy [fm]
xx [fm]
dt = 1.5 * 10-24s
Impact parameter = 0.0 fmImpact parameter = 0.0 fm
TDHF calculation of neutron-rich TDHF calculation of neutron-rich nucleinuclei
51.8MeV
![Page 17: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/17.jpg)
Total densityTotal density
Different contact time for N Different contact time for N & P& P
Neutron densityNeutron density
Proton densityProton density
7
7
Contact time for N & P is Contact time for N & P is differentdifferent
Estimated contact time = Estimated contact time = 7.0 7.0 dt dt for Nfor N
Estimated contact time = Estimated contact time = 8.0 8.0 dt dt for Pfor P
dt = 1.5 * 10-24s
20
10
0
30
Composite nucleiComposite nuclei
x x [fm]yy [fm]
Already contactedAlready contacted
Passing Passing throughthrough
Time (Time (*dt [sec]))
![Page 18: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/18.jpg)
Observation of the early accelerationObservation of the early acceleration
timetimetimetime
Early acceleration in stable-unstable Early acceleration in stable-unstable collisioncollision
Velocity [(2/3)* 10Velocity [(2/3)* 1099 m/s] m/s] Velocity [(2/3)* 10Velocity [(2/3)* 1099 m/s] m/s]
AccelerationAcceleration AccelerationAcceleration
which is found in the motion of lighter nuclei
Neutrons of projectileNeutrons of projectile Protons of projectileProtons of projectile
![Page 19: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/19.jpg)
Different scattering for Different scattering for N N andand P P inside “the inside “the neutron skin”neutron skin” dt = 1.5 * 10-24s
20
10
0
30
Composite nucleiComposite nuclei
xx [fm]
Already contactedAlready contacted
Time (Time (*dt [sec]))
Passing Passing throughthrough
yy [fm]
Trace of nucleon @ He (calculated result)Trace of nucleon @ He (calculated result)
t t = 0.0= 0.0
yy [f
m]
xx [fm]
Center of mass motion = Trace of neutron @ Center of mass motion = Trace of neutron @ HeHe
neutronneutron
protonprotont t = 30.0= 30.0
t t = 10.0= 10.0
t t = 20.0= 20.0
t t = 7.0= 7.0
t t = 10.0= 10.0
magnifymagnify
yy [f
m]
xx [fm]
t t = 5.0 = 5.0 ~~ 10.010.0passing neutron skinpassing neutron skin
neutronneutron
protonprotonneutron skin of Ca targetneutron skin of Ca target
![Page 20: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/20.jpg)
t t = 20.0= 20.0
nucleon @ projectilenucleon @ projectile
PP
pp
nn
nn projectileprojectile
Early state of 4 nucleons in projectileEarly state of 4 nucleons in projectile
pp++ nn++
pp-- nn--
rather distant correlationrather distant correlation
Description of projectileDescription of projectile
No significant difference for “t = 13.0 to 20.0”.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 nucleonsIt is due to the Pauli effect between originally 4+4 1s-nucleons, than from other nucleons
t t = 13.0= 13.0
neutronneutronprotonproton
(it does not mean weak)(it does not mean weak)
IndexIndex : sign of Jz: sign of Jz
yy [f
m]
xx [fm]
neighboring correlationneighboring correlation
Deuteron neighboring pictureDeuteron neighboring picture(n(n++, p, p++) ------ (n) ------ (n--, p, p--))alwaysalways
![Page 21: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/21.jpg)
4He +40Ca
xx [fm]
TDHF calculation of non-zero impact TDHF calculation of non-zero impact parameterparameter
Impact parameter =Impact parameter = 4.518 fm4.518 fm
Initial energy
(E/A = 0.7MeV)
30.8MeV
xx [fm]
(Almost the radius of (Almost the radius of 4040Ca)Ca)
tt = = 0.0(s)0.0(s) xx [fm]
yy [f
m]
yy [f
m]
Deuteron neighboring pictureDeuteron neighboring picture
Center of mass motionCenter of mass motion
For comparisonFor comparison
neutronneutronprotonproton
Velocity [(2/3)* 10Velocity [(2/3)* 1099 m/s] m/s]
timtimee
Neutrons of projectileNeutrons of projectile
accelerationacceleration
L-S force dominantL-S force dominant
smallsmall
![Page 22: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/22.jpg)
4He +70Ca
tt = = 0.0(s)0.0(s)
yy [fm]
xx [fm] dt = 1.5 * 10-24s
TDHF calculation of neutron-rich TDHF calculation of neutron-rich nucleinuclei
Impact parameter =Impact parameter = 6.668 fm6.668 fm
Initial energy
(E/A = 0.7MeV)
51.8MeV
The The samesame
xx [fm]
(Almost the radius of (Almost the radius of 7070Ca)Ca)
![Page 23: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/23.jpg)
Different contact time for N Different contact time for N & P& P
20
10
0
30
xx [fm]
40
14
14
Contact time for N & P is Contact time for N & P is differentdifferent
Estimated contact time = Estimated contact time = 14.0 14.0 dt dt for Nfor N
Estimated contact time = Estimated contact time = 15.5 15.5 dt dt for Pfor P
Neutron densityNeutron density
Proton densityProton density
dt = 1.5 * 10-24s
Time (Time (*dt [sec]))
![Page 24: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/24.jpg)
Early accelerations are clearly weakened, when Early accelerations are clearly weakened, when
timetimetimetime
Velocity [(2/3)* 10Velocity [(2/3)* 1099 m/s] m/s] Velocity [(2/3)* 10Velocity [(2/3)* 1099 m/s] m/s]
It is mainly due to that Pauli effectPauli effect is not so effective
0b
relative to the case of head-on collision (full overlap case).
In this neutron-rich case,In this neutron-rich case,
Neutrons of projectileNeutrons of projectile Protons of projectileProtons of projectile
NeutronNeutron ProtonProton
we can say that there is we can say that there is no accelerationno acceleration for projectile any more !! for projectile any more !!
![Page 25: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/25.jpg)
dt = 1.5 * 10-24s
20
10
0
30
xx [fm]
Time (Time (*dt [sec]))Impact parameter =Impact parameter = 6.668 fm6.668 fm
40
neutronneutronprotonproton
yy [f
m]
xx [fm]
t t = 0.0= 0.0
Center-of-mass motionCenter-of-mass motion
““Brand new” different scatteringBrand new” different scattering
t t = 24.0= 24.0Neutron skinNeutron skin
t t = 30.0= 30.0
t t = 35.0= 35.0
Di-neutron & di-proton neighboring pictureDi-neutron & di-proton neighboring picture
Isospin-difference dominantIsospin-difference dominant
![Page 26: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/26.jpg)
nucleon @ projectilenucleon @ projectile
PP
pp
nn
nn projectileprojectile
Early state of 4 nucleons in projectileEarly state of 4 nucleons in projectile
It is due to the Neutron rich effectIt is due to the Neutron rich effect (← unbalance between N& P) (← unbalance between N& P)
pp++ nn++
pp-- nn--
neighboring correlationneighboring correlation
rather distant correlationrather distant correlation
Description of projectileDescription of projectile
neutronneutronprotonproton
IndexIndex : sign of Jz: sign of Jz
yy [f
m]
xx [fm]
t t = 24.0= 24.0
t t = 30.0= 30.0
Di-neutron & di-proton pictureDi-neutron & di-proton picture
![Page 27: 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.](https://reader034.fdocuments.in/reader034/viewer/2022052702/56649f3f5503460f94c5fb70/html5/thumbnails/27.jpg)
SummarySummary Relative large early accelerations are seen mainly in head-onhead-on collisions.
Frequently found states of projectile in the very early timeFrequently found states of projectile in the very early time
00 Contactable or notContactable or not
4 nucleons of 4 nucleons of projectileprojectile
Impact parameter and neutron-richness dependence can be seen
bb[fm][fm]
nnnn / n/ nz z ( = neutron richness of target )( = neutron richness of target )
Di-neutron & di-proton pictureDi-neutron & di-proton picture
Deuteron pictureDeuteron picture
Di-neutron & di-proton pictureDi-neutron & di-proton pictureDeuteron pictureDeuteron picture
protonprotonneutronneutron
Near the “drip line”Near the “drip line”
Deuteron pictureDeuteron picturePauli scattering
(large acceleration)““stable line”stable line”
small acceleration
→ → Large acceleration is due to the Pauli effect (with full overlap) Large acceleration is due to the Pauli effect (with full overlap)
in the neighboring property neighboring property of projected 4 nucleons.
Single centerSingle center