Relationship of equilibrium distributions of excited nuclei in deformation coordinate and their fission rate in the case of canonical ensemble

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


Release:

2015, Vol. 1. №3(3)

Title: 
Relationship of equilibrium distributions of excited nuclei in deformation coordinate and their fission rate in the case of canonical ensemble


About the author:

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

Abstract:

Classical Kramers formulas for fission rate of excited nuclei are widely used in the combined modeling of this process. In the scientific literature there is evidence that when using these formulas, the fission rate can have uncontrolled errors, the size of which can reach 20% or even more. In this paper the relationship between the fission rate of the nuclei and their equilibrium distribution in the deformation coordinate is analyzed. Based on the results of the analysis performed, a correction to Kramers formulas that allows to reduce significantlly the error of analytically calculated fission rate for some collective potentials is introduced. The case of using the canonical ensemble in the model of fission is considered. Application of the proposed methodology to reach the agreement of Kramers and dynamical quasistationary fission rates will significantly reduce the errors of the combined simulation of nuclear fission.

References:

1.             Adeev G. D., Karpov A. V., Nadtochij P. N., Vanin D. V. Mnogomernyj stohasticheskij podhod k dinamike delenija vozbuzhdjonnyh jader [Multidimensional Stochastic Approach to Fission Dynamics of Excited Nuclei] // Fizika jelementarnyh chastic i atomnogo jadra [Physics of Elementary Particles and Atomic Nuclei]. 2005. Vol. 36. P. 731. (In Russian)

2.             Gonchar I. I. Lanzhevenovskaja fluktuacionno-dissipativnaja dinamika delenija vozbuzhdjonnyh atomnyh jader [Langevin Fluctuation-Dissipation Dynamics of Fission of Excited Atomic Nuclei] // Fizika jelementarnyh chastic i atomnogo jadra [Physics of Elementary Particles and Atomic Nuclei]. 1995. Vol. 26. P. 922. (In Russian)

3.             Gonchar I. I. Teoreticheskoe issledovanie zavisimosti srednego vremeni delenija vozbuzhdennyh atomnyh jader ot uglovogo momenta [Theoretical Investigation of the Angular-momentum Dependence of the Mean Fission Lifetime of Excited Nuclei] // Jadernaja fizika [Physics of Atomic Nuclei]. 2004. Vol. 67. P. 2101. (In Russian)

4.             Gonchar I. I. Mnogomernaja dinamichesko-statisticheskaja model' delenija vozbuzhdjonnyh jader [Multidimentional Dynamical-statistical Model of Excited Nuclei Fission] // Jadernaja fizika [Physics of Atomic Nuclei]. 2000. Vol. 63. P. 1778.
(In Russian)

5.             Demina E. G., Gonchar I. I. Tochnost' priblizhennyh formul Kramersa dlja skorosti delenija: kanonicheskij i mikrokanonicheskij ansambli [Accuracy of the Approximate Kramers Formulas for the Fission Rate: Canonical and Microcanonical Ensembles] // Jadernaja fizika [Physics of Atomic Nuclei]. 2014. Vol. 77. P. 882. (In Russian)

6.             Eremenko D. O. Dinamiko-statisticheskij podhod k opisaniju reakcii vynuzhdennogo delenija tjazhjolyh jader [Combined Dynamical and Statistical Approach to Describing Induced Fission of Heavy Nuclei] // Jadernaja fizika [Physics of Atomic Nuclei]. 2009. Vol. 72. P. 1707. (In Russian)

7.             Litnevskij A. L., Gonchar I. I. Analiz vlijanija formy kollektivnogo potenciala v oblasti spljusnutyh form jadra na kvazistacionarnuju skorost' delenija. Popravka k klassicheskim formulam Kramersa [The Analysis of the Impact of the Collective Potential Shape in the Oblate Nuclear Configurations Region on the Quasistationary Fission Rate. The Correction Factor to the Classical Kramers’s Formulas] // Vestnik ToGU [PNU Herald]. 2015. No 1(36). P. 17. (In Russian)

8.             Gontchar I., Litnevsky L.A., Frцbrich P. 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 Communications. 1997. No 107. P. 223.

9.             Kramers H. A. Brownian motion in a field of force and the diffusion model of chemical reactions // Physica. 1940. Vol. 7. P. 284.

10.         Gontchar I. I., Chushnyakova M. V., Aktaev N. E., Litnevsky A. L., Pavlova
E. G. Disentangling effects of potential shape in the fission rate of heated nuclei // Physical Review. 2010. Vol. 82. Pp. 604-606.