Fusion and quasifission dynamics
in the synthesis of superheavy elements
Lu GuoUniversity of Chinese Academy of Sciences, Beijing

China-Japan collaboration workshop,
Tsukuba University, 26-28 June, 2017

Contents
I. Introduction
background for SHE and TDHF

II. Fusion and quasifission dynamics
neutron-rich target 48Ca+239Pu and 48Ca+244Pu

III. Multi-nucleon transfer reaction
production of new neutron-rich isotopes

IV. Summary and perspectives

Synthesis of SHE
Ways to synthesize heavy and superheavy elements:
 neutron capture:
94Pu---100Fm;

existence of longlived SHE island?

 light ions (1H, 2H, 3H, He) colliding on target:
heaviest to 101Md
 multi-nucleon transfer (MNT)
 fusion reactions
 cold fusion: with 208Pb and 209Bi as target, to 113Nh
 hot fusion: with 48Ca as projectile, to 118Og
The synthesized SHE are neutron-deficient andMNT reaction productfar from the predicted stable SHE island.

238U fission productHIC with heavy nuclei
targetprojectile

HIC with heavy nuclei
targetcaptureprojectile

HIC with heavy nuclei
targetcapturefusionprojectile

quasifission

HIC with heavy nuclei
deexcitation of neutrontargetcapture

fusionsurvival
superheavy
element

projectile

quasifission

fissionthe time for quasifission ~10-20s, fusion-fission ~10-20 ~10-16s
Quasifission is the primary mechanism to prevent the formation of superheavy elements.

HIC with heavy nuclei
deexcitation of neutron

targetcapturefusionsurvival
superheavy
element

projectile

quasifission

fissionFusion probability
 Phenomenological model
 DNS
 Langevin-type equation
 fusion by diffusion model Grazing model ......


Microscopic model
 QMD
 TDHF ......

 The PCN given by phenomenological model is different by several order; The PCN can’t be measured directly in experiments;
 Microscopic model would be better;

Time-dependent Hartree-Fock theory
 time-dependent Hartree-Fock (TDHF) theory
S=

∫

t2t1

Ψ (t ) | H − i∂ t | Ψ (t ) dt，=
Ψ (r1 , r2 , , rA , t )H=AA∑ t +∑ v=i 1ii< jij

Ef∂ϕ1，i λ hϕλdet ϕλ ( ri , t)=∂tA!

Advantages：
 Fully microscopic, parameter-free theory in heavy-ion collisions; Nuclear structure and reactions in a unified framework (same EDF);
 Dynamical and quantum effects are automatically incorporated;

Limitations： Only one-body dissipation;
 tunneling effect is missing;10

TDHF EDF in fusion dynamics
 Energy density functional (EDF)
Both time-even and time-odd EDF have been included

H0 is basic functional used in Sky3D code and most TDHF calculations

Quasifission dynamics in experiments

 An experiment measure the fragment’s mass-angle correlations in 40,48Ca +238U；
 The studies show an unexpected interplay between the orientation of
the prolate deformed 238U with quantum shell effects.

Quasifission dynamics in experiments

 An experiment measure the fragment’s mass-angle correlations in 40,48Ca +238U；
 TDHF calculations show that for 48Ca projectiles the quasifission is substantiallyreduced in comparison to the 40Ca case. This partly explains the success ofsuperheavy element formation with 48Ca beams；

Contents
I. Introduction
background for SHE and TDHF

II. Fusion and quasifission dynamics
neutron-rich target 48Ca+239Pu and 48Ca+244Pu

III. Multi-nucleon transfer reaction
production of new neutron-rich isotopes

IV. Summary and perspectives

Experimental Synthesis of SHE 114

Experimental Synthesis of SHE 114

Experimental Synthesis of SHE 114

Experimental Synthesis of SHE 114

Experimental Synthesis of SHE 114

Experimental Synthesis of SHE 114

Zagrebaev et al., PRC85,014608(2012);
Adamian et al., PRC69,014607(2004);

TDHF studies of fusion and quasifission
48Ca+239Pu with E =204.02 MeV, b=2.5 fm
cm

TDHF studies of fusion and quasifission
48Ca+244Pu with E =216.76 MeV, b=2.0 fm
cmTDHF studies of fusion and quasifission
48Ca+239Pu(1) Collisions with the tip of 239Pu produce
quasifission fragments, while collisions
with the side result in fusion；(2) contact time decreases as b;(3) tip:
side:

32Ge+82Pb
40Zr+74W;(4) The interplay between quantum shell effectand orientation of deformed nuclei;

TDHF studies of fusion and quasifission
48Ca+239Pu

48Ca+244Pu

(1) The collision 48Ca+239Puis much easier to happen quasifission than 48Ca+244Pu (experiment),

TDHF studies of fusion and quasifission(2) More neutron-rich target nucleus will be helpful in the production of SHE(ANU experiments);
48Ca+239Pu
48Ca+244Pu(3) PCN=σfus/σcap , PCN=0.2 2(48Ca+244Pu), PCN=0.14 (48Ca+239Pu)---side (first microscopic PCN);TDHF studies of fusion and quasifission
Mass-angle distribution: directly measured by experimentsθ=θin + θTDHF + θ out

TDHF studies of fusion and quasifission
Mass-kinetic distribution: directly measured by experiments

Systematic agreement with the Viola formula;
Quasifission dynamics is a fully damped motion;

Contents
I. Introduction
background for SHE and TDHF

II. Fusion and quasifission dynamics
neutron-rich target 48Ca+239Pu and 48Ca+244Pu

III. Multi-nucleon transfer reaction
production of new neutron-rich isotopes

IV. Summary and perspectives

Multi-nucleon transfer reaction
The experiments via multi-nucleon transfer reaction to produce neutron-rich heavy nuclei

美国Argone

德国GSI

日本KEK俄罗斯DUBNA

154

Sm +150 Nd → 122

154

Sm +154 Sm → 124

fusion diffusion modelσ ∼ 0.6 pb

σ ∼ 10−13 pb

30

Neutron-rich isotopes production
 New neutron-rich isotope production via multi-nucleon transfer
154

Sm +160 Gd ?
→ 126

Ning Wang and Lu Guo, Phys. Lett. B760, 236 (2016).

31

Neutron-rich isotopes production
Isotope distribution at different impact parameters

Ning Wang and Lu Guo, Phys. Lett. B760, 236 (2016).

32

SummaryThree-dimensional TDHF with full Skyrme functional and without
any symmetry restrictions; The fusion and quasifission dynamics in 48Ca+239Pu and 48Ca+244Pu;
Our results qualitatively explains the experimental observations; Multi-nucleon transfer reactions produce the new neutron-rich nuclei;

SummaryThree-dimensional TDHF with full Skyrme functional and without
any symmetry restrictions; The fusion and quasifission dynamics in 48Ca+239Pu and 48Ca+244Pu;
Our results qualitatively explains the experimental observations; Multi-nucleon transfer reactions produce the new neutron-rich nuclei;

Thank you for your attention!

Quantum Molecular Dynamics Model Quantum Molecular dynamics (QMD)=φi ( r )ri =

 ( r − ri ) 2
i+ r ⋅ pi exp  −22 3/ 4

4σ r

( 2πσ r )1∂H,∂pi = − ∂HPi∂riAdvantages
 Microscopic theory in heavy-ion collisions; Both mean field and collision terms inlcuded;

Limitations
 Pauli principle
 Shell effects
 antisymmetrization of wave functions
35

deexcitation of neutron

targetcaptureprojectile

fusionsurvival

superheavy
elementtransferor DICquasifission

fission