Quasifission reactions in heavy ion collisions at low energies A.K. Nasirov 1, 2 1 Joint Institute for Nuclear Research, Dubna, Russia 2 Institute of Nuclear Physics, , Tashkent, Uzbekistan September 1, 2015 Trento “Interfacing Structure and Reaction Dynamics in the Synthesis of the Heaviest Nuclei” at the ECT*, Trento, Italy, September 1-4, 2015

Synthesis of superheavy elements in the cold and hot fusion reactions. 2

Quasifission is a binary process producing two reaction products in heavy ion collisions. The basic difference between fusion fission and quasifission is that compound nucleus formation is not achieved in the latter mechanism. Quasifission can be thought of as a bridge between deep-inelastic scattering, where the relative kinetic energy between the fragments can be partially damped, but the mass asymmetry of the entrance channel is mostly preserved, and compound nucleus fission reactions.

Total kinetic energy Mass distribution Mass distribution Angular distribution Fusion-fission Viola systematics with small fluctuations Gaussian like shape with shape with structure structure Mainly isotropic Mainly isotropic + Anisotropic (L) (L, t K ) (L, t K ) Quasifission Viola systematics with large fluctuations Asymmetric- double gaussian (L, t DNS ) (L, t DNS )Anisotropic + isotropic (new) (L, t DNS ) (L, t DNS ) Fast-fission ? ? Mainly isotropic Comparison of characteristics of reaction fragments

Reaction channels in heavy ion collisions at low energies 5 (Superheavy element) Complete fusion

Dependence of the formation of fission-like binary fragments on the orbital angular momentum, L Fast fission 0 < L < L B 0 < L < L cap L B < L < L cap L= I ω

Mass-energetic distribution of the binary products in heavy ion collisions Deep inelastic collisions Quasifission Fusion-fission

Mechanisms of the reaction following after capture (capture means formation of dinuclear system): Fusion-fission, quasifission and fast-fission.

Progress in study of the quasifission reactions The mass distribution of the quasifission products is peaked near the masses of the target and of the projectile. The fraction of the mass distribution located at symmetry is relatively small. The fragment kinetic energies are characteristic of the Coulomb repulsion of fission fragments. The angular distributions are peaked in the vicinity of the grazing angle. Phys.Rev.Lett. 36, 18 (1976)

Full damped (capture) and partially damped (deep-inelastic collision) events. diffusion effects on nucleons angular dependence of energy loss

Mass-angle distribution as function of the beam energy in 63 Cu+ 197 Au reaction. C. Ngô et al, Nucl.Phys. A267, 181 (1976). The increase of the beam energy leads to the shift of the mass distribution of the reaction products to the small angles.

α=M 1 t is maximum of the mass distribution as a function of time ; Γ 2 is the square of the width (FWHM) related with diffusion coefficient.

13 Dynamics of complete fusion and a role of the entrance channel in formation of reaction products in heavy ion collisions are questionable or they have different interpretation still now. For example, -- what kind of fusion mechanism makes a main contribution to the formation of compound nucleus: the increase of the neck between interacting nucleus, or multinucleon transfer at relatively restricted neck size, or + ? The details of angular momentum distribution of dinuclear system and compound nucleus those determine cross sections of evaporation residue, fusion-fission and quasifission products; The theoretical and experimental studies are important in order to clarify the origin of fission events (CN-fission against quasifission), namely, to separate fusion-fission fragments from the quasifission and fast- fission products. What is questionable in fusion-fission reactions ?

` II. Quasifission: 1) Full momentum transfer; 2) Equilibrium of energy distribution and mass distribution; 3) Anisotropic and isotropic angular distributions. III. Compound nucleus formation: 1) Full momentum transfer; 2) Equilibrium of energy distribution and mass distribution; 3) Isotropic angular distributions. b b b Formation of the dinuclear system ( Capture reactions) I. Deep inelastic collisions: 1)Partial momentum transfer; 2)There is not equilibrium of energy distribution and mass distribution; 3)Anisotropic angular distribution Beam

Interpretation of the mechanism of production radioisotopes with different energy at SHIP 64 Ni Pb S. Heinz, V. Comas, F. P. Heßberger, S. Hofmann, D. Ackermann, et al. Eur. Phys. Jour. A 38, 227 (2008) “Di-nuclear systems studied with the velocity filter SHIP” Mass – charge and angular distributions of the multinucleon transfer reaction were estimated.

The role of nuclear shell effects in the yield of the quasifission products.

Mixing of the distribution of fragment masses versus total kinetic energy Experimental data from Ref. W.Q. Shen et al (GSI) Phys.Rev.C36, 115 (1987), where two reaction products of deep-inelastic collisions (DIC), quasifission (QF) and fusion-fission (FF) processes are registered for three reactions at three values of beam energy 5.4, 6.7, 7.5 MeV A. 70 Zn DIC FF QF DIC QF

18 А – deep inelastic collision products В- quasifission products Z 1 =20 Z 2 =82 Mixing products formed in the deep-inelastic collisions and quasifission Z Z G. Fazio et al.,Mod. Phys. Lett. Vol. 20, No. 6 (2005) 391

19 Comparison of theoretical results with the experimental data for the capture, fusion and evaporation residue excitation functions G. Fazio, et al. Modern Phys. Lett. A 20, No. 6 (2005)

20 The observed decrease of the quasifission contribution by increase of the collision energy in 48 Ca+ 154 Sm reaction. (from paper Knyazheva G.N. et al. Phys. Rev. C 75, (2007).

Evolution of the mass distributioin of quasifission fragments 21

22 TKE=K 1 +K 2 P(M 1,M 2.TKE) P(M 1,M 2 )= Σ P(M 1,M 2.TKE) = Σ TKE P(M 1,M 2.TKE)

Explanation of the lack of quasifission fragment yields at the expected place of mass distribution in the 48 Ca+ 144 Sm reaction

24 Comparison of the capture, fusion-fission and quasifission cross sections obtained in this work with data from experiments Knyazheva G.N. et al. Phys. Rev. C Vol. 75. –P (13). and evaporation residues Stefanini A.M. et al. Eur. Phys. J. A –2005. Vol. 23. –P.473

The role of the angular momentum of dinuclear system in competition between complete fusion and quasifission.

The lifetime and rotational angle of the dinuclear system formed in 48 Ca+ 154 Sm reaction as a function of the E c.m. energy.

The overlap of the angular momentum distributions of the fusion-fission and quasifission processes.

Comparison of the potential wells of the nucleus-nucleus interaction for reactions leading to formation of 220 Th. 28 B qf

Importance of the radial and tangential friction coefficients

A new problem in separation of fusion-fission and the quasifission products in heavy ion collisions when there is overlap their mass and angular distributions. The partial quasifission excitation function calculated at different values of the collision energy E c.m. for the 32 S W reaction.

The analysis of experimental data deals with the limiting value of angular momentum CN for complete fusion, as in paper by R.S. Naik et al. Phys. Rev. C 76, (2007). The use of this formula assumes that the quasifission products are not formed in collisions with angular momentum L < L CN. 31

32 The methods of calculation of the capture and fusion cross section in the dinuclear system approach.

The evaporation residue cross section (synthesis of superheavy element) is calculated by the well known expression: is fusion probability which calculated by the methods of dinuclear system concept N.A. Antonenko et al., Phys. Lett. B 319, 425 (1993);Phys. Rev. C 51, 2635 (1995); G. Adamian, N.V. Antonenko, and W. Scheid, Eur. Phys. J. A 41, 235 (2009); A. K. Nasirov et al. Phys. Rev. C 79, (2009). is capture probability, which calculated in different theoretical models by different way. A. K. Nasirov et al., Nucl. Phys.A759, 342 (2005). K. Kim et al., Phys.Rev. C 91, (2015). 33

34 Equations of motion used to find the capture of projectile by target- nucleus

Nucleus-nucleus interaction potential 35

36 Hamiltonian for calculation of the transport coefficients of collective motion G.G. Adamian, et al. Phys. Rev. C56 No.2, (1997) p A.K. Nasirov, Thesis of the Doctor of Science, 2004, Institute of Nuclear Physics, Tashkent

Density dependent effective nucleon-nucleon forces 37 The values of the constants of the effective nucleon-nucleon forces from the textbook A.B. Migdal, “Theory of the Finite Fermi-Systems and properties of Atomic Nuclei”, Moscow, Nauka, The constants of version II were used in our calculations.

Comparison of the friction coefficients, calculated by different methods Solid line – G.G. Adamian, et al. PRC 56 (1997) 373 Long dashed -- Short dashed- - Dotted - Temperatura= 2 MeV Temperatura= 1 MeV Temperatura= 0.5 MeV By Yamaji et al(microscopic): S. Yamaji and A. Iwamoto, Z. Phys. A 313, (1983) 161.

Calculation of the competition between complete fusion and quasifission: P cn (E DNS,L) 40 Nasirov A.K. et al. Nuclear Physics A 759 (2005) 342–369 Fazio G. et al, Modern Phys. Lett. A 20 (2005) p.391

Nucleon transfer coefficients for evolution of the charge asymmetry of dinuclear system 41 G.G. Adamian, et al. Phys. Rev. C53, (1996) p R.V. Jolos et al., Eur. Phys. J. A 8, 115–124 (2000)

A new problem in separation of fusion-fission and the quasifission products in heavy ion collisions when there is overlap their mass and angular distributions. The partial quasifission excitation function calculated at different values of the collision energy E c.m. for the 32 S W reaction.

Comparison of the partial fusion cross sections of the 40 Ar+ 180 Hf and 82 Se+ 138 Ba reactions leading to the same compound nucleus 220 Th K. Kim et al. Phys.Rev.C 91, (2015) (a) (b) (d) (c)

Fusion hindrance increases by increasing the orbital angular momentum. F 44 Dependence of the driving potential and quasifission barrier on the angular momentum of dinuclear system formed in reactions leading to formation of compound nucleus 216 Th. PHYSICAL REVIEW C 72, (2005) U dr = B 1 + B 2 - (B CN + V CN (L )) + V (A, Z, ß 1, α 1 ; ß 2, α 2 ; R,L)

45 Calculation of the life time of dinuclear system

46 Collective enhancement of level density of DNS

Description of the observed angular anisotropy of the fissionlike products.

Estimation of the quasifission contribution in the observed angular anisotropy of the fissionlike products. A.K. Nasirov, et al. Eur. Phys. J. A 34, 3 25–339 (2007) B. John, S.K. Kataria, Phys.Rev.C 57, 1337 (1998) B.B. Back et al, Phys. Rev.Lett. 50, 818 (1983)

Statistical calculation of the anisotropy of the angular distribution A.K. Nasirov, et al. Eur. Phys. J. A 34, 325–339 (2007)

50 Partial fusion cross section as a function of the orientation of axial symmetry axis reactants Nasirov A.K. et al. The role of orientation of nuclei symmetry axis in fusion dynamics, Nucl. Phys. A 759 (2005) 342

52 Dependence of the driving potential (а) and quasifission barrier (b) on the mutual orientations of the axial symmetry axes of nuclei A.K. Nasirov, et al.Nucl. Phys. A 759 (2005) 342

Conclusions 1.One of version of the dinuclear system model is being developed to study entrance channel dynamics of heavy ion collisions at the near Coulomb barrier energies. 2.Dynamics of the macroscopic and microscopic degrees of freedom can be calculated by analysis of the coupling term connecting them. As a result we find transport coefficients for the relative motion. 3.Method developed by us allows to calculate partial and total cross sections of the capture and fusion of colliding nuclei, as well as decay of the formed dinuclear system (quasifisson). 4.The angular momentum distribution of the compound nucleus is used by the advanced statistical code to calculate the evaporation residue cross sections, particularly, the cross sections synthesis of superheavy nuclei. 5.The anisotropy in the angular distribution of the fusion-fission and quasifission fragments can be is studied by analyzing the angular-momentum distributions of the dinuclear system and compound nucleus which are formed after capture and complete fusion, respectively.