8^th International Workshop on Nuclear Dynamics in Heavy-ion Reactions 

The effect of the entrance channels on the dynamics of the competition of processes of the nuclear reactions in heavy-ion collisions.

А.К. Nasirov^1,2, B. M. Kayumov ^2,3, G. A. Yuldasheva², E.D. Khusanov^2,4

¹Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, Russia

²Institute of Nuclear Physics, Academy of Science of Uzbekistan

³New Uzbekistan University, Tashkent, Uzbekistan

⁴National University of Uzbekistan, Tashkent

August 21-25, 2026, Shanxi, China

Content

1. Introduction
2. Different approaches in study of the hindrance to complete fusion.
3. Application of the dinuclear system model to explain the results of mixing of quasifission and fusion-fission products.
4. Unexpected low cross section in synthesis of darmstadium in hot fusion reaction 48Ca+232Th.
5. Conclusions.

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History: International School-Seminar on Heavy Ion Physics in Dubna, Flerov Laboratory of Nuclear Reactions, JINR, September 1993.

Vadim Volkov, Gurgen Adamian, Nikolai Antonenko,

and Avazbek Nasirov

Avazbek Nasirov, Gurgen Adamian, Wolf Udo Schroeder, Evgeni Cherepanov, and Nikolai Antonenko,

The authors of the dinuclear system model: N.V. Antonenko, E.A. Cherepanov, A.K. Nasirov, V.P. Permjakov, V.V. Volkov

Reasons causing a hindrance to formation of the evaporation residues in synthesis of the superheavy elements complete fusion.

Competition between quasifission and formation of the compound nucleus is the other reason causing decreasing of the probability of synthesis of superheavy elements. The quasifission is dominant in cold fusion processes.

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N.V. Antonenko, V.V. Volkov, E.A. Cherepanov, A.K. Nasirov, V.P. Permyakov

Phys.Lett. B 319 (1993) p.425; Phys.Rev.C 51, (1995) p.2635. For first time

Fusion

Quasifission

P_CN=1

Two different mechanisms of the complete fusion.

Multinucleon transfer mechanism of the complete fusion

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1. The extra push model was developed by W.J. Swiatecki

[Phys. Scripta 24, 113 (1981); Nucl. Phys. A 376, 275 (1982)] and

extra-extra push model [J. Błocki, H. Feldmeier, W.J. Świątecki, Nucl. Phys. A 459 (1986) 145.] was suggested to describe the experimental values of the fusion cross sections in the reactions with the massive nuclei.

​

2. The models in this direction have been developed later to include the dynamical effects at calculation of the nucleus-nucleus potential:

Washiyama K. and Lacroix D. Phys. Rev. C 78 024610 (2008)

Washiyama K., Lacroix D. and Ayik S. Phys. Rev. C 79 024609 (2009)

Long Zhu et al., Nucl. Phys. A 915, 90–105 (2013).

3. ….

The hindrance to complete fusion in the nuclear reactions of the heavy ion

collisions is seen from the calculations of the fusion cross sections which

depend on the nucleus-nucleus interaction potential.

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Appearance of the hindrance to complete fusion (P_CN< 1) in the nuclear reactions of the heavy ion collisions.

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Incomplete fusion (ICN)

F₁

F₂

L_ICN

E*_ICN

Potential energy surface of for two colliding nuclei

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Main reaction channels of the heavy ion collisions

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Incomplete fusion (ICN)

F₁

F₂

L_ICN

E*_ICN

Mass-energetic distribution �of the binary products

Deep inelastic collisions

Quasifission

Fusion-fission

​

The dinuclear system concept assumes that nucleon transfer between two nuclei is main mechanism of the nuclear reactions in heavy-ion collisions at the around Coulomb barrier energies.

Superheavy elements

Sketch of the reaction mechanisms:

dinuclear system, mononucleus and compound nucleus are always

have alternative ways for their evolution.

Beam

Detectors

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Meenu Thakur et al. Eur. Phys. J. A 53, 133 (2017)

About mixing of the reaction products in different reaction channels

“Competing asymmetric fusion-fission and quasifission in neutron-deficient sub-lead nuclei”, S. Gupta, ..., A.K. Nasirov, G.A. Yuldasheva, Phys. Lett. B 803, 135297 (2020).

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Classical equations of the radial and tangential motions with the friction coefficients which are calculated microscopically.

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E^*_DNS

Theoretical framework for the charge and mass distributions

Master equation:

A.K.Nasirov, B.M.Kayumov, O.K.Ganiev, G.A.Yuldasheva, Phys. Lett. B, 842, 137976, 2023

The proton number in

the light fragment

The proton number

in the heavy fragment

Calculation of the yields of the quasifission products at breakup of the dinuclear system

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Nasirov A.K. et al. Eur. Phys. Jour. A 34, 325 (2007)

γ = 8 · 10 ^{− 22} MeV sec ^{− 1}

A.K. Nasirov INP

Role of quasifission in fission fragment mass distributions for �the ²⁸Si + ¹⁹⁷Au reaction.

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The role of the quasifission contribution in the dependence of the width of the mass distribution of fission-like products on the collision energy.

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P

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b

¹⁸O

¹⁸O

⁴He

⁴He

¹⁶⁵Ho

¹⁶⁵Ho

¹⁷⁹Ta

E*_DNS

E*’_DNS

Incomplete fusion

E*’’_DNS

Calculation of the incomplete fusion cross section

А.К.Nasirov, et. al. Phys. Lett. B 942 (2023) 137976

A.K. Nasirov INP

The role of the orbital angular momentum

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A,Z

A_C, Z_C

Conjugate

nucleus

Application of the dinuclear system model for the interpretation of the experimental data measured at the Inter-University Accelerator Centre (IUAC), New Delhi by the group of �Prof. Indranil Mazumdar from Tata Institute of Fundamental Research, Mumbai, India.

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A.K. Nasirov INP

The appearance of the hindrance to complete fusion in reactions with the light nuclei due to centrifugal forces in collisions with the large impact parameters.

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¹⁶O+¹³⁰Te

L=40 h

R=R_m(Z)

Z,A

Z_tot-Z

R

(A.K. Nasirov et al. Physics Letters B 842: 137976 (2023))

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Solutions of the transport master equations for the evolution and decay dinuclear system formed in reaction ¹⁸O+¹⁶⁵Ho.

(A.K. Nasirov et al. Physics Letters B 842: 137976 (2023))

Comparison of the results by dinuclear system model and PACE4 code used in Ref. Avinash Agarwal, et al. Phys.Rev.C103-034602 (2021).

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Fig.6. from Avinash Agarwal, et al. Phys.Rev.C103, 034602 (2021).

Comparison of theoretical result (curve) of this work with experimental data (squares).

A.K. Nasirov INP

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Differences in the cross sections of the evaporation residues of the same superheavy elements, obtained

for cold and hot fusion reactions, shows the dependence of the fission barrier on neutron numbers.

Fission barrier of the superheavy elements

as a function of their neutron numbers.

⁴⁸Ca+²³²Th

Nc=170

⁶⁴Ni+²⁰⁸Pb,

Nc=162

⁶⁴Ni+²⁰⁹Bi, Nc=160

⁴⁸Ca+²³⁷Np

Nc=172

N_comp=170

N_comp=160

PHYSICAL REVIEW C 110, 014618 (2024)

A.K.N., A. R. Yusupov, and B. M. Kayumov. Small cross section of

the synthesis of darmstadtium in the ⁴⁸Ca+²³²Th reaction.

M. Kowal, et al. Phys.Rev.C 82, 014303 (2010).

Conclusion

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1. Experience of the synthesis of superheavy elements shows that there is

a huge hindrance for complete fusion of the colliding nuclei as a function of

the mass asymmetry of the entrance channel.

2. The hindrance to fusion increases by the increase of the angular momentum

of collision.

3. Incomplete fusion occurs as the hindrance to complete fusion in collisions with

the angular momentum of collision.

4. Complete fusion occurs by multinucleon transfer through the neck connecting

two fragments of dinuclear system.

A.K. Nasirov INP

Thank you for your attention !

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Calculation of the competition between complete fusion and quasifission: P_cn(E_DNS,L).�Influence of the nuclear shell effects are in intrinsic barrier B*_fus and in Y_Z charge (mass) distributions.

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Kayumov B.M., Ganiev O.K., A.K. N, G.A. Yuldasheva

Phys. Rev. C 105, 014618 (2022)

Nasirov A.K. et al. Nuclear Physics A 759 (2005) 342.

Fazio G. et al, Modern Phys. Lett. A 20 (2005) p.391

E*_DNS(Z)=E_c.m.-V_min+(B_P+B_T) -(B_Z+B_ztot-z)

B_P,B_T, B_Z, B_ztot-z are binding energies of the colliding nuclei

and fragments of the dinuclear system.

Shell structure data of nuclei are included

into calculation of potential energy surface due

to these quantities.