The Approximation of the Time Dependence of Excited Nuclei Fission Rate on the Smooth Function

Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy


2016, Vol. 2. №2

The Approximation of the Time Dependence of Excited Nuclei Fission Rate on the Smooth Function

About the author:

Andrey L. Litnevsky, Cand. Sci. (Phys.-Math.), Omsk State Technical University;


The paper discusses the main advantages and disadvantages of the three types of excited atomic nuclei fission models: statistical, dynamical, and combined, focusing on statistical modeling. One of the main problems of this approach to the theoretical study of the nuclear process fission is the incorrect consideration of the relaxation stage of the fission rate time dependence. In order to get rid of this disadvantage of the statistical models, it is required to use the correct method of analytical calculation of the time dependence of the nuclear fission rate.

The article presents the first step to solving this problem: a method of approximation of the excited nuclei fission rate time dependence by a smooth function based on the Woods-Saxon function. The modification of this dependence consists in adding into its formula a parameter responsible for the change of the diffuseness by time. The selection of this parameter allows to achieve the consent of analytical and dynamic dependencies on the relaxation stage of fission rate. Calculating values of approximating function parameters is carried out by the method of least squares. A quantitative assessment of the consistency of the approximating functions with dynamic dependence is given.

In conclusion, recommendations for further research are formulated. The use of the obtained results in further statistical modeling of excited atomic nuclei fission may allow to conduct a more realistic simulation with fewer errors.


  1. Adeev G. D., Gonchar I. I., Pashkevich V. V., Pischasov N. I., Serdyuk O. I. 1988. “Diffuzionnaya model formirovaniya raspredeleniy oskolkov deleniya” [Diffusion Model of the Distribution of Fission Fragments]. Physics of Elementary Particles and Atomic Nuclei, vol. 19, p. 1229.
  2. Adeev G. D., Karpov A. V., Nadtochiy P. N., Vanin D. V. 2005. “Mnogomernyy stokhasticheskiy podkhod k dinamike deleniya vozbuzhdennykh yader” [Multidimensional Stochastic Approach to Fission Dynamics of Excited Nuclei]. Physics of Elementary Particles and Atomic Nuclei, vol. 36, p. 731.
  3. Aktaev N. E., Gonchar I. I. 2010. “Dinamicheskoe i statisticheskoe modelirovanie protsessa deleniya vysokovozbuzhdennykh atomnykh yader s uchetom relaksatsionnoy stadia” [Dynamic and Statistical Modeling of the Process of Fission of Atomic Nuclei Highly Considering the Relaxation Stage]. Bulletin of the Russian Academy of Sciences. Physics, vol. 74, no 4, p. 545.
  4. Blann M., Komoto T. T. 1984. “Computer Codes ALERT I and ALERT II”. Lawrence Livermore National Laboratory.
  5. Bohr N., Wheeler J. A. 1939. “The Mechanism of Nuclear Fission”. Physical Review, vol. 56, p. 426. DOI: 10.1103/PhysRev.56.426
  6. Chaudhuri G., Pal S. 2002. “Prescission Neutron Multiplicity and Fission Probability from Langevin Dynamics of Nuclear Fission”. Physical Review C, vol. 65. DOI: 10.1103/PhysRevC.65.054612
  7. Gontchar I., Litnevsky L. A., Fröbrich P. 1997. “A C-Code for Combining a Langevin Fission Dynamics of Hot Nuclei with a Statistical Model Including Evaporation of Light Particles and Giant Dipole γ-Quanta”. Computer Physics Communication, vol. 107, p. 223. DOI: 10.1016/S0010-4655(97)00108-2
  8. Hasse R. W. 1969. “Dynamical Model of Asymmetric Fission”. Nuclear Physics A, vol. 128, p. 609. DOI: 10.1016/0375-9474(69)90426-6
  9. Litnevskiy A. L., Gonchar I. I. 2015. “Analiz vliyaniya formy kollektivnogo potentsiala v oblasti splyusnutykh form yadra na kvazistatsionarnuyu skorost deleniya. Popravka k klassicheskim formulam Kramersa” [Analysis of the Influence of the Collective Capacity in the Core to Form Flattened Quasi-Stationary Fission Rate. Amendment to Kramers’ Classical Formulas]. Bulletin of Pacific National University, no 1 (36), p. 17.
  10. Tillack G.-R. 1992. “Two-Dimensional Langevin Approach to Nuclear Fission Dynamics”. Physics Letters B, vol. 278, p. 403. DOI: 10.1016/0370-2693(92)90575-O