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

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Abstract:

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.

References:

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