4C EOS and Heavy Nuclei, ARIS2014

2014.6.6 (Fri.)@ Univ. of Tokyo

Repulsive aspects of pairing correlationin nuclear fusion reaction
Shuichiro Ebata

Meme Media Laboratory, Hokkaido Univ.
Nuclear Reaction Data Centre, Hokkaido Univ.
(JCPRG)

Takashi Nakatsukasa
Center for Computational Sciences and Faculty of Pure and Applied Sciences, Univ. of Tsukuba
Theoretical Nuclear Physics Laboratory, RIKEN Nishina Center

ARIS2014, 14.6.6
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Simulation of heavy ion collision using TDHF
H.Flocard, S.E.Koonin and M.S.Weiss Phys. Rev. C17 (1978) 1682

ARIS2014, 14.6.6
S.EbataSeveral mean-field theories

No Pairing

For static

For dynamics

Hartree-Fock(HF)

Time-Dependent HF(TDHF, RPA)WithBCS Pairing

HF+BCSWith Pairing

Hartree-FockBogoliubov(HFB)※ RPA: Random-Phase Approximation※ QRPA: Quasi-particle RPA
ARIS2014, 14.6.6
S.Ebata

TDHF+BCS

Cb-TDHFBTDHFB(QRPA)

What kind of pairing effect is expected
in low-energy Heavy ion collision ?
W.J.Swiatecki, Phys. Rev. 100 (1955) 937.

Fusion or Fission cross section
Level crossing
Energy Dissipation
Neck formation
Odd-even effects
for spontaneous fission half-lives ?
Pair transfer reaction
Nuclear Josephson effect

ARIS2014, 14.6.6
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SpontaneousFission Half-lives

Method S.E. et al.: PRC82 (2010) 034306
Statics: HF+BCS
Dynamics: Cb-TDHFB
ph-channel Int. : Skyrme (SkM*, SLy4d)
pp(hh)-channel : δ - type (time-reversal): spin-singlet zero-range interaction

Points:To solve Cb-TDHFB in 3D space enable us
to study nuclear dynamics including
deformation and pairing, self-consistently.
For the simulation of collisionPrepare the target and projectile nuclei
with HF+BCS, put them with some b anddistance, also add velocity to them, andtheir time will be evolved by Cb-TDHFB.

Cb-TDHFB Eqs.
: Canonical basis (for l also): Occupation Prob. (for l >0): Pair Prob. (for l >0)

ARIS2014, 14.6.6
S.EbataExample : Photo-absorption cross section of 172Yb
3D Cb-TDHFB
Cb-TDHFB can reproduce
the photo-absorption cross section of 172Yb.

β =0.32∆n = 0.76 [MeV]∆p = 0.55 [MeV]

Heavy nucleus
Deformed nucleus
Including pairingΓ= 1.0 [MeV]

Dipole mode

K=0-Proton

Total cal. cost : 300 CPU hours(with a Single processor; Intel Core i7 3.0 GHz)
Box size : R=15[fm], mesh=1[fm] (3D-Spherical)

Canonical-basis space (HF+BCS g.s.) :146 states for neutron,
98 states for proton
Experimental data:
A.M.Goryachev and G.N.Zalesnyy Vopr. Teor. Yad. Fiz. 5, 42 (1976).

ARIS2014, 14.6.6
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K=1-NeutronSetup for collision
Incident Energy : 18 - 20 [MeV] (Ecm = 9.0 – 10 [MeV], VCoul. ~ 9 MeV)
Impact parameter : 2.8 - 3.1 [fm]Effective Interaction : Skyrme force (SkM*), Contact pairing
Projectile : 22O, Target : 22O (HF g.s. has also spherical shape)# of canonical-basis for HF+BCS g.s. ; (N, Z) = (32 (16+16) , 16 (8+8))
Average of gap energy ;Calculation space (3D meshed box):
Length of box for ( x, y, z )is 36, 20, 40[fm] meshed by 1.0 [fm]ARIS2014, 14.6.6
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Simulation of 22O + 22O collision with b = 3.0 [fm] and Ecm=10 [MeV]Time-evolution of Neutron density distribution
Cb-TDHFB

TDHF

ARIS2014, 14.6.6
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Simulation of 22O + 22O collision with b = 3.0 [fm] and Ecm=10 [MeV]Time-evolution of Neutron density distribution
Cb-TDHFB

TDHF

ARIS2014, 14.6.6
S.EbataFromsimulation of 22O + 22O collision with b = 2.8 – 3.1 [fm] and Ecm=10 [MeV],

Pairing correlation does not increase the fusion cross section (in this work).
Up to now

Same nuclei collision with the incident energy around Coulomb barrier→ Pairing correlation can have repulsive aspects in fusion reaction.
σH ~ 283 mb → σB ~ 246 mb be small about 15%→ The repulsive effects depends on the strength of pairing.
From now on
In a little bit heavier system?
← To increase pair number
Case of different nuclei collision? ← Large difference of chemical potential
will accelerate Pair transfer.
Is the pairing effects visible in much heavier system?

ARIS2014, 14.6.6
S.EbataIn a little bit heavier system
Projectile : 52Ca, Target : 52Ca

Point: increase of pair number

In both methods, the g.s. is spherical shape.

Ecm = 51.5 MeV (VCoul. ~ 49 MeV)

Impact parameter : 2.2 - 2.6 [fm]Effective Interaction : SkM*, Contact pairing
To reproduce ∆n of 52Ca
Cb-TDHFBTDHF→ σH ~ 189 mb → σB ~ 181 mb be small about 5%
ARIS2014, 14.6.6
S.EbataIn a little bit heavier system
Projectile : 52Ca, Target : 52Ca

Point: increase of pair number

In both methods, the g.s. is spherical shape.

Ecm = 51.5 MeV (VCoul. ~ 49 MeV)

Impact parameter : 2.2 - 2.6 [fm]Effective Interaction : SkM*, Contact pairing
To reproduce ∆n of 52Ca
Cb-TDHFBTDHF→ σH ~ 189 mb → σB ~ 181 mb be small about 5%
ARIS2014, 14.6.6
S.EbataCase of different nuclei collision
Projectile : 22O, Target : 52Ca

Point:
Difference of chemical potential

In both methods, the g.s. is spherical shape.

Ecm = 25 MeV (VCoul. ~ 20.8 MeV)

Impact parameter : 3.0 - 4.5 [fm]Effective Interaction : SkM*, Contact pairing
Average of strength in 22O and 52Ca
Cb-TDHFB

TDHF→ σH ~ 528 mb → σB ~ 503 mb be small about 5%
ARIS2014, 14.6.6
S.EbataCase of different nuclei collision
Projectile : 22O, Target : 52Ca

Point:
Difference of chemical potential

In both methods, the g.s. is spherical shape.

Ecm = 25 MeV (VCoul. ~ 20.8 MeV)

Impact parameter : 3.0 - 4.5 [fm]Effective Interaction : SkM*, Contact pairing
Average of strength in 22O and 52Ca
Cb-TDHFB

TDHF→ σH ~ 528 mb → σB ~ 503 mb be small about 5%
ARIS2014, 14.6.6
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Is the pairing effect visible in much heavier system ?
Projectile : 96Zr, Target : 124Sn

HF+BCS : Both ground states are spherical shape.
Ecm = 228 MeV (Vcoul. =216, 225 MeV) HF : 96Zr ; spherical, 124Sn ; oblate shape.

Effective Interaction : SLy4d, Contact pairing
Very strong in order to check the effect
Neglect proton pairing

HF g.s. of 124Sn has Oblate shape. β =-0.1

Coulomb barrier for 96Zr+124Sn (F.D.)

96Zr

Sn124

VFD=225 MeV
96Zr

Sn124

VFD=216 MeV
ARIS2014, 14.6.6
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Is the pairing effect visible in much heavier system ?
TDHF (z || Z)

TDHF (x,y || Z)

Cb-TDHFBARIS2014, 14.6.6
S.EbataIs the pairing effect visible in much heavier system ?
TDHF (x,y || Z)

Time up to scission

Cb-TDHFB<TDHF (z || Z)!!
ARIS2014, 14.6.6
S.EbataSummary & Perspective
Simulation of the collision phenomena with Cb-TDHFB
We apply Cb-TDHFB to large amplitude collective phenomena such as collision,
with a contact pairing functional.
22
O+22O : Pairing effects in fusion reaction, have a repulsive aspects.
52
Ca+52Ca : The repulsive aspect appears also, but its contribution becomes small.
22O+52Ca : The similar aspects can be seen.
96Zr+124Sn : The pairing effects gets the time from a contact to scission to be short.

Perspectiverof
To analyze the detail of internal behaviorouy!
kMore accurate calculation
nnoiathnTet
Behavior of single-particle levels in real-time cal.
tar
Energy distribution, Level crossingyou
100

NeutronProton

80
60
40
200
Particle number projection for the multi-particle transfer
in real-time cal.
78

Nucleon transfer (Pair transfer), Nuclear Josephson effects
ARIS2014, 14.6.6S.Ebata

910111213Particle number1415

1617