LowLow--energy fusionenergy fusion--fission dynamics fission dynamics of heavy nuclear systemsof heavy nuclear systems

ValeryValery ZagrebaevZagrebaev

•• Unified description of DeepUnified description of Deep--Inelastic, QuasiInelastic, Quasi--Fission and FusionFission and Fusion--Fission processesFission processes

•• What can we learn from experiments on DeepWhat can we learn from experiments on Deep--Inelastic scattering ?Inelastic scattering ?

•• QuasiQuasi--fission, Fusion and Superfission, Fusion and Super--Heavy Element formationHeavy Element formation

•• Collisions of very heavy ions ( U + Cm, Collisions of very heavy ions ( U + Cm, …… ) at low energies) at low energies

•• New experiments scheduled in New experiments scheduled in DubnaDubna for 2006for 2006

JINRJINR ((DubnaDubna))

Strongly coupled Strongly coupled Deep Inelastic, QuasiDeep Inelastic, Quasi--Fission, and FusionFission, and Fusion--Fission processesFission processes

DiabaticDiabatic and Adiabatic Potential Energyand Adiabatic Potential Energy

What is behavior of valence neutrons What is behavior of valence neutrons in nearin near--barrier fusion reactions ?barrier fusion reactions ?

Wave functions of valence neutrons follow the two-center molecular states and spread over both nuclei before they reach and overcome the Coulomb barrier !

→TwoTwo--Center Shell ModelCenter Shell Model and and Adiabatic Potential Energy SurfaceAdiabatic Potential Energy Surfaceare appropriate for descriptionare appropriate for descriptionof such processes.of such processes.

Time-dependent Schrödinger equationfor valence neutron wave function

Shortcoming of MacroShortcoming of Macro--Microscopic Potential EnergyMicroscopic Potential Energy

Variables ? Potential Energy ? Equations of Motion ?Variables ? Potential Energy ? Equations of Motion ?

Potential Energy: Fusion, Fission and QuasiPotential Energy: Fusion, Fission and Quasi--FissionFission

Equations of Motion. The problem of mass exchangeEquations of Motion. The problem of mass exchange

The system of coupled The system of coupled LangevinLangevin type Equations of Motiontype Equations of Motion

OrientationOrientation effectseffects

Cross sections and decay of primary fragmentsCross sections and decay of primary fragments

Collisions of heavy nuclei (no CN formation)Collisions of heavy nuclei (no CN formation)

8686Kr + Kr + 166166Er Er collisioncollision at at EEcmcm = 464 = 464 MeVMeV ( Coulomb ( Coulomb barrierbarrier = 260 = 260 MeVMeV ))

8686Kr + Kr + 166166Er Er collisioncollision at at EEcmcm = 464 = 464 MeVMeV ( Coulomb ( Coulomb barrierbarrier = 260 = 260 MeVMeV ))

8686Kr + Kr + 166166Er Er collisioncollision at at EEcmcm = 464 = 464 MeVMeV ( ( time analysis time analysis ))

What can we learn ?What can we learn ?

4848Ca + Ca + 248248Cm Cm collisioncollision at at EEcmcm = 203 = 203 MeVMeV ( ( oneone trajectorytrajectory ))

4848Ca + Ca + 248248Cm Cm collisioncollision at at EEcmcm = 203 = 203 MeVMeV

Predictive power of the theoryPredictive power of the theory

2002 ( 3n ? 4n ? )

2003: theoretical predictions

Collision of very heavy (Collision of very heavy (transactinidetransactinide) nuclei ?) nuclei ?

Production of Production of neutronneutron--rich rich superheavysuperheavy nuclei nuclei

and giant quasiand giant quasi--atomsatoms

normal (symmetrizing)

quasi-fission

“inverse”(antisymmetrizing)

quasi-fission

Production of neutronProduction of neutron--rich rich superheavysuperheavy nuclei and giant quasinuclei and giant quasi--atomsatoms

Comparison with available experimental dataComparison with available experimental data

DeepDeep--Inelastic and QuasiInelastic and Quasi--Fission processes in veryFission processes in very--heavyheavy--ion damped collisionsion damped collisions

Isotopic yield of SHE in veryIsotopic yield of SHE in very--heavyheavy--ion damped collisionsion damped collisions

Experiments to be performed in Experiments to be performed in DubnaDubna in 2006in 2006

• Fusion of fission fragments: 136Xe + 136Xe → 272108

• Synthesis of 120: 54Cr + 248Cm → 302120

136136Xe + Xe + 136136Xe Xe →→ 272272108108

136136Xe + Xe + 136136Xe Xe →→ 272272108108

Synthesis of Synthesis of 302302120120

Cross sections of the reactions leading to Cross sections of the reactions leading to 302302120120

•• For heavy nuclear system it is extremely important to perform For heavy nuclear system it is extremely important to perform a a combined (unified) analysiscombined (unified) analysis of all strongly coupled channels: of all strongly coupled channels: DeepDeep--Inelastic scattering, QuasiInelastic scattering, Quasi--Fission, Fusion and regular Fission. Fission, Fusion and regular Fission. This ambitious goal has now become possible.This ambitious goal has now become possible.

•• A unified potential energy surface and a unified set of dynamic A unified potential energy surface and a unified set of dynamic equations are proposed equations are proposed for the simultaneous description of DI and Fusionfor the simultaneous description of DI and Fusion--Fission processes. Fission processes. For the first time the whole evolution of the heavy nuclear systFor the first time the whole evolution of the heavy nuclear system can be tracedem can be traced starting starting from the approaching stage and ending in DI, QF, and/or Fusionfrom the approaching stage and ending in DI, QF, and/or Fusion--Fission channels.Fission channels.

•• Accurate estimations of the probabilities for Accurate estimations of the probabilities for supersuper--heavy elementheavy element formation can be obtained formation can be obtained now. The mechanisms of quasinow. The mechanisms of quasi--fission and fusionfission and fusion--fission processes can be clarified much fission processes can be clarified much better than before . Determination of such fundamental characterbetter than before . Determination of such fundamental characteristics of nuclear dynamics istics of nuclear dynamics as the as the nuclear viscositynuclear viscosity and the and the nucleon transfer ratenucleon transfer rate is now possible.is now possible.

•• Low energy collisions of Low energy collisions of transuraniumtransuranium nuclei: nuclei: Production of longProduction of long--lived neutronlived neutron--rich SHE rich SHE seems to be quite possible due to a large seems to be quite possible due to a large mass and charge rearrangement in the mass and charge rearrangement in the ““inverse quasiinverse quasi--fissionfission”” process caused process caused by the Z=82 and N=126 nuclear shells. by the Z=82 and N=126 nuclear shells. Spontaneous positron emission from a supercritical electric fielSpontaneous positron emission from a supercritical electric fieldd of longof long--lived quasilived quasi--atoms atoms formed in these reactions is also quite expected.formed in these reactions is also quite expected.… many other possibilities …

SummarySummary