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II. Fusion and quasifission with the dinuclear system model

Second lecture. II. Fusion and quasifission with the dinuclear system model. Contents. Introduction Models for fusion with adiabatic and diabatic potentials Dynamics of fusion in the dinuclear system model Quasifission and incomplete fusion Summary and conclusions. Work of

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II. Fusion and quasifission with the dinuclear system model

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  1. Second lecture II. Fusion and quasifission with the dinuclear system model

  2. Contents • Introduction • Models for fusion with adiabatic and diabatic potentials • Dynamics of fusion in the dinuclear system model • Quasifission and incomplete fusion • Summary and conclusions

  3. Work of G. G. Adamian, N. V. Antonenko, R. V. Jolos, S. P. Ivanova, A. Zubov Joint Institute for Nuclear Research, Dubna Collaboration with Junqing Li, Wei Zuo, Institute of Modern Physics, Lanzhou Enguang Zhao, Ning Wang, Shangui Zhou Institute of Theoretical Physics, Beijing

  4. Introduction Superheavy elements are presently produced in heavy ion reactions up to element 118. Experiments done at GSI (Darmstadt), JINR (Dubna), GANIL (France), LBNL (Berkeley), RIKEN (Japan), IMP(Lanzhou) Two types of reactions are successful: Cold and hot complete fusion reactions with excitation energies of the compound nucleus of E*CN of 12-15 and 32-36 MeV, respectively.

  5. a) Lead-based cold fusion reactions 70Zn+208Pb278112277112+n, =1 pb E*CN  12 MeV for Z108 b) Hot fusion reactions with 48Ca projectiles 48Ca+244Pu292114289114+3n, =1 pb E*CN  32 MeV Small cross sections: Competition between complete fusion and quasifission

  6. Idea of Volkov (Dubna) to describe fusion reactions with the dinuclear system concept: Fusion is assumed as a transfer of nucleons (or clusters) from the lighter nucleus to the heavier one in a dinuclear configuration. This process is describable with the mass asymmetry coordinate =(A1-A2)/(A1+A2). A1 A2 If A1 or A2 get small, then ||1 and the system fuses.

  7. The dinuclear system model uses two main degrees of freedom to describe the fusion and quasifission processes: Relative motion of nuclei, capture of target and projectile into dinuclear system, decay of the dinuclear system: quasifission Transfer of nucleonsbetween nuclei, change of mass and charge asymmetries leading to fusion and quasifission

  8. Aim of lecture: • Consideration of the fusion dynamics, • comparison of models in the calculation of residue cross sections for superheavy nuclei, • discussion of quasifission with master equations, • incomplete fusion as a signature for the dinuclear model.

  9. 2. Models for fusion with adiabatic and diabatic potentials • Heavy and superheavy nuclei can be produced by fusion reactions with heavy ions. • Two main collective coordinates are used for the description of the fusion process: • Relative internuclear distance R • Mass asymmetry coordinate h for transfer

  10. Description of fusion dynamics depends strongly whether adiabatic or diabatic potential energy surfaces are assumed. V diabatic adiabatic R touching configuration

  11. Diabatic potentials are repulsive at smaller internuclear distances R<Rt. Explanation with two-center shell model: i i 2 2 1 1 R R adiabatic model diabatic model Velocity between nuclei leads to diabatic occupation of single-particle levels, Pauli principle between nuclei

  12. diabatic adiabatic l~R

  13. Models using adiabatic potentials • Minimization of potential energy, essentially adiabatic potential in the internuclear distance, nuclei melt together. R 0 Large probabilities of fusion for producing nuclei with similar projectile and target nuclei.

  14. h entrance quasifission fusion touching configuration R

  15. 48Ca + 246Cm (from Zagrebaev)

  16. b) Dinuclear system (DNS) concept Fusion by transfer of nucleons between the nuclei (idea of V. Volkov, also von Oertzen), mainly dynamics in mass asymmetry degree of freedom, use of diabatic potentials, e.g. calculated with the diabatic two-center shell model. h 1

  17. h 1 fusion entrance quasifission touching configuration to R

  18. 58Fe+244Pu 302120

  19. 110Pd+ 110Pd TCSM double folding ~R

  20. 2R0

  21. Calculation of diabatic potential: = single particle energies = occupation numbers Diabatic occupation numbers depend on time: De-excitation of diab. levels with relaxation time, depending on single particle width.

  22. diabatic adiabatic

  23. 3. Dynamics of fusion in the dinuclear system model Evaporation residue cross section for the production of superheavy nuclei:

  24. Partial capture cross section scap • Dinuclear system is formed at the initial stage of the reaction, kinetic energy is transferred into potential and excitation energy. V(R) Bqf=barrier for quasifission R touching point

  25. b) Probability for complete fusion PCN DNS evolves in mass asymmetry coordinate by diffusion processes toward fusion and in the relative coordinate toward the decay of the dinuclear system which is quasifission. V(h) B*fus h -1 hi 1 B*fus=inner fusion barrier

  26. 222Th

  27. Competition between fusion and quasifission, both processes are treated simultaneously. Calculation of PCN and mass and charge distributions in h and R: Fokker-Planck equation, master equations, Kramers approximation.

  28. c) Kramers formula for PCN: Rate for fusion:  fus Rate for quasifission: qf = R + sym, i.e. decay in R and diffusion in  to more symmetric DNS. Cold fusion (Pb-based reactions): Hot fusion (48Ca projectiles):

  29. d) Importance of minima in the driving potential Shell and deformation effects lead to local minima in V(). In liquid drop model the mean value of  runs to symmetric fragmentation: , then quasifission. Minima in V() hinder motion to , then larger probability for fusion. Idea of A. Sandulescu and W. Greiner (1976) for optimum selection of target and projectile: choice of fragmentations in minima of V().

  30. A. Sandulescu and W. Greiner (1976) 102 114 110 106 100 104 112 108

  31. Z=114 Z=108

  32. Example: 54Cr + 208Pb  262Sg V(h) B*fus Bsym h 54Cr + 208Pb B*fus=5.7 MeV, Bsym=3.6 MeV, Bqf=2.7 MeV Dependence of fusion probability PCN on barrier height Bsym.

  33. B*fus Bsym 54Cr + 208Pb  262Sg

  34. e) Optimum excitation energy for Pb-based fusion reactions V(h) B*fus E*CN h hi -1 1 E*CN = Ecm + Q V(hi) + B*fus

  35. Cold fusion

  36. f) Survival probability Wsur De-excitation of excited compound nucleus by neutron emission in competition with fission. Other decays (g-, a-decays) can be neglected. For Pb-based reactions with emission of one neutron: Gn =width for neutron emission Gf =fission width, Gf>> Gn P1n =probability of realisation of 1n channel

  37. g) Results for cold fusion reactions Cold reactions: AZ+208Pb superheavy + n

  38. nb pb fb

  39. 110 67 112 68 68 70 114 76 73

  40. 76Ni+208Pb 64Ni+208Pb

  41. ANi+208Pb110

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