NEW SERIES. SERIES: PHYSICS

Izvestiya of Saratov University.

ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)


Cite this article as:

Litnevsky V. L., Ivanyuk F. A., Kosenko G. I. Research of the Possibility of Freezing Some Degrees of Freedom of the System in the Calculation of the Collision Process of Atomic Nuclei. //Izvestiya of Saratov University. New series. Series: Physics. , 2020, vol. 20, iss. 3, pp. 233-242. DOI: https://doi.org/10.18500/1817-3020-2020-20-3-233-242

Published online: 
31.08.2020
Language: 
Russian
UDC: 
539.172.17

Research of the Possibility of Freezing Some Degrees of Freedom of the System in the Calculation of the Collision Process of Atomic Nuclei

Abstract: 

Background and Objectives: A large number of theoretical and experimental papers have been devoted to the study of the fusionfission reaction of heavy ions. This is primarily due to the fact that these reactions allow us to obtain superheavy nuclei or exotic isotopes that lie far from the beta-stability line. To describe these reactions, you must be able to describe the collision process of the initial nuclei. Moreover, the accuracy of the entrance channel description affects the quality of all subsequent modeling results. Recently, a number of works have appeared that seek to take into account all possible deformations and orientations when calculating the interaction of colliding atomic nuclei. At the same time, increasing the number of system shape parameters taken into account (increasing the dimension of the space of collective coordinates of the system) increases the complexity of performing dynamic calculations. So, the purpose of this work is to find an approximation that takes into account the main physical processes that occur when two atomic nuclei collide, but does not lead to serious complication of calculations. Materials and Methods: In this paper, we consider the collision of atomic nuclei in the hot fusion reactions 36S + 238U and 64Ni + 238U. To model this process, a dynamic stochastic model is used. It takes into account the shell structure of colliding cores and their mutual orientation in space. Four deformation parameters are used to describe the shape of the system under consideration. The dynamic evolution of these parameters is described in the framework of the Langevin equations. Results: The paper discusses the possibility of freezing some of the degrees of freedom of the system. It is shown that a relatively heavy target nucleus, deformed in the ground state, weakly changes its deformation and orientation in space during the evolution of the system up to the transition through the Coulomb barrier. The numerical results are compared with the experimental data. Conclusion: The prohibition of the evolution of the target nucleus deformation and orientation degrees of freedom does not significantly affect the simulation results, namely, the probability of the system passing through the Coulomb barrier and the distance between the centers of mass of colliding nuclei at the moment of the penetration through the Coulomb barrier. The choice of the reactions under consideration allows us to judge the effect of the mass of the projectile nucleus on the results of calculations, and also allows us to generalize the results obtained in the present work to a wide range of reactions with the mass ratio of colliding nuclei lying in the range from 0.15 to 0.27. Most of the reactions currently used for the synthesis of superheavy elements are in this range.

DOI: 
10.18500/1817-3020-2020-20-3-233-242
References: 
  1. Kozulin E. M., Knyazheva G. N., Novikov K. V., Itkis I. M., Itkis M. G., Dmitriev S. N., Oganessian Yu. Ts., Bogachev A. A., Kozulina N. I., Harca I., Trzaska W. H., Ghosh T. K. Fission and quasifi ssion of composite systems with Z = 108–120: Transition from heavy-ion reactions involving S and Ca to Ti and Ni ions. Phys. Rev. C, 2016, vol. 94, pp. 054613. DOI: https://doi.org/10.1103/PhysRevC.94.054613
  2. Nishio K., Ikezoe H., Mitsuoka S., Nishinaka I., Nagame Y., Watanabe Y., Ohtsuki T., Hirose K., Hofmann S. Effects of nuclear orientation on the mass distribution of fi ssion fragments in the reaction of 36S+238U. Phys. Rev. C, 2008, vol. 77, pp. 064607. DOI: https://doi.org/10.1103/PhysRevC.77.064607
  3. Dvorak J., Brüchle W., Chelnokov M., Dressler R., Düllmann Ch. E., Eberhardt K., Gorshkov V., Jäger E., Krücken R., Kuznetsov A., Nagame Y., Nebel F., Novackova Z., Qin Z., Schädel M., Schausten B., Schimpf E., Semchenkov A., Thörle P., Türler A., Wegrzecki M., Wierczinski B., Yakushev A., Yeremin A. Doubly Magic Nucleus 270Hs. PRL, 2006, vol. 97, pp. 242501. DOI: https://doi.org/10.1103/PhysRev-Lett.97.242501
  4. Karpov A. V., Saiko V. V. Modeling near-barrier collisions of heavy ions based on a Langevin-type approach. Phys. Rev. C, 2018, vol. 96, pp. 024618. DOI: https://doi.org/10.1103/PhysRevC.96.024618
  5. Adamian G. G., Antonenko N. V., Lenske H., Malov L. A. Predictions of identifi cation and production of new superheavy nuclei with Z=119 and 120. Phys. Rev. C, 2020, vol. 101, pp. 034301. DOI: https://doi.org/10.1103/Phys-RevC.101.034301
  6. Fröbrich P. Fusion and capture of heavy ions above the barrier: analysis of experimental data with the surface friction model. Phys. Rep., 1984, vol. 116, pp. 337–400. DOI: https://doi.org/10.1016/0370-1573(84)90162-5
  7. Marten J., Fröbrich P. Langevin description of heavyion collisions within the surface friction model. Nucl. Phys. A, 1992, vol. 545, pp. 854–870. DOI: https://doi.org/10.1016/0375-9474(92)90533-P
  8. Volcov V. V. Process of Complete Fusion of Atomic Nuclei. Complete Fusion of Nuclei in the Framework of the Dinuclear System Concept. Phys. Part. Nucl., 2004, vol. 35, pp. 425–486.
  9. Saiko V. V., Karpov A. V. Analysis of multinucleon transfer reactions with spherical and statically deformed nuclei using a Langevin-type approach. Phys. Rev. C, 2019, vol. 99. pp. 014613. DOI: https://doi.org/10.1103/PhysRevC.99.014613
  10. Litnevsky V. L., Kosenko G. I., Ivanyuk F. A., Chiba S. Description of the mass-asymmetric fission of the Pt isotopes, obtained in the reaction 36Ar+142Nd within the two-stage fusion-fission model. Phys. Rev. C, 2019, vol. 99, pp. 054624. DOI: https://doi.org/10.1103/Phys-RevC.99.054624
  11. Davydovska O. I., Denisov V. Yu., Nesterov V. A. Comparison of the nucleus-nucleus potential evaluated in the double-folding and energy density approximations and the cross-sections of elastic scattering and fusion of heavy ions. Nucl. Phys. A, 2019, vol. 989, pp. 214–230. DOI: https://doi.org/10.1016/j.nuclphysa.2019.06.004
  12. Ismail M., Ellithi A. Y., Botros M. M., Mellik A. E. Azimuthal angle dependence of Coulomb and nuclear interactions between two deformed nuclei. Phys. Rev. C, 2007, vol. 75, pp. 064610. DOI: https://doi.org/10.1103/PhysRevC.75.064610
  13. Litnevsky V. L., Kosenko G. I., Ivanyuk F. A. Allowance for the Tunnel Effect in the Entrance Channel of Fusion–Fission Reactions. Phys. At. Nucl., 2016, vol. 79, no. 3, pp. 342–450.
  14. Litnevsky V. L., Kosenko G. I., Ivanyuk F. A., Pashkevich V. V. Description of synthesis of super-heavy elements within the multidimentional stochastic model. Phys. Rev. C, 2014, vol. 89. pp. 034626. DOI: https://doi.org/10.1103/PhysRevC.89.034626
  15. Pashkevich V. V. On the asymmetric deformation of fissioning nuclei. Nucl. Phys. A, vol. 169, pp. 275–293. DOI: https://doi.org/10.1016/0375-9474(71)90884-0
  16. Adeev G. D., Karpov A. V., Nadtochy P. N., Vanin D. V. Multidimensional stochastic approach to the fi ssion dynamics of excited nuclei. Phys. Part. Nucl., 2005, vol. 36, pp. 387–426.
  17. Strutinsky V. M. Shell effects in nuclear masses and deformation energy. Nucl. Phys. A, 1967, vol. 95, pp. 420–442. DOI: https://doi.org/10.1016/0375-9474(67)90510-6
  18. Ivanyuk F. A., Ishizuka C., Usang M. D., Chiba S. Temperature dependence of shell corrections. Phys. Rev. C, 2018, vol. 97, pp. 054331. DOI: https://doi.org/10.1103/PhysRevC.97.054331
  19. Iljinov A. S., Mebel M. V., Bianchi N., De Sanctis E., Guaraldo C., Lucherini V., Muccifora V., Polli E., Reolon A. R., Rossi P. Phenomenological statistical analysis of level densities, decay widths and lifetimes of excited nuclei. Nucl. Phys. A, 1992, vol. 543, pp. 517–554. DOI: https://doi.org/10.1016/0375-9474(92)90278-R
  20. Hofmann H., Kiderlen D. A Self-Consistent Treatment of Damped Motion for Stable and Unstable Collective Modes. Int. J. Mod. Phys. E, 1998, vol. 7, pp. 243–274. DOI: https://doi.org/10.1142/S0218301398000105
  21. Kurmanov R. S., Kosenko G. I. New approach to calculating the potential energy of colliding nuclei. Phys. At. Nucl., 2014, vol. 77, pp. 1442–1452.
  22. Koura H., Yamada M. Single-particle potentials for spherical nuclei. Nucl. Phys. A, 2000, vol. 671, pp. 96–118. DOI: https://doi.org/10.1016/S0375-9474(99)00428-5
  23. Hasse R. W., Myers W. D. Geometrical Relationships of Macroscopic Nuclear Physics. Heidelberg, SpringerVerlag, 1988. 116 p.
  24. Zu-Hua L., Jing-Dong B. The effects of deformation and orientation of colliding nuclei on synthesis of superheavy elements. Nucl. Phys. A, 2019, vol. 991, pp. 121616. DOI: https://doi.org/10.1016/j.nuclphysa.2019.121616
  25. Hofmann H. A quantal transport theory for nuclear collective motion: The merits of a locally harmonic approximation. Phys. Rep., 1997, vol. 284, iss. 4–5, pp. 137–380. DOI: https://doi.org/10.1016/S0370-1573(97)00006-9​
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