NON-EQUILIBRIUM STATISTICAL THEORY OF NUCLEAR FISSION MASS DISTRIBUTION

  • We consider the fission process from saddle point to scission point as a non-equili-brium transport process obeying the Master equation, which can be reduced into theform of Fokker-Planck equation approximately. Taking the mass asymmetry coordinatex as the macrovariable, the nuclear fission can be considered as a diffusion process inx space, the drift velocity v(x,t), which is a non-linear. function of x, is proportionalto the gradient of the potential surface of fission nucleus in x space. The kinetics ofnuclear deformation from saddle point to scission point is represented by the variationof v(x,t) with time t phenomenologically. Assuming the mass distribution at saddlepoint is a symmetric one, and to solve the Fokker-Planck equation by means of Su-zuki's scaling limit approximation method, we get a solution which becomes a double-Gaussian asymmetric distribution on the potential valley after a time interval longenough, the width of mass distribution is proportional to nuclear temperature and in-versely proportional to relative depth of the potential valley. In the case of 235U(n,f),the time interval evaluated from saddle point to scission point would be larger than1.6×10-21 second, while it has arrived at the statistical equilibrium state. The Fong'sstatistical theory of nuclear fission is proved to be the case of stationary solution of theFokker-Planck equation exactly.
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  • [1] M. Brack, J. Damgaard,A. S. Jensen, H. C. Pauli, V. M. SVrutinsky and C. Y. Wong, Rev. Mod. Phys.,44(1972), 320.[2] P. Fong, Phys. Rev., C13(1976), 1259.[3] J. R. Nix, Nucl. Phys., A130(1969), 241.[4] P. Fong, Phys. Rev., 102(1956), 434.[5] P. Fong, Phys. Rev., 136(1984), B1338;C17(1978), 1731.[6] S. Ayik, B. Schiirmann and W. Norenberg, Z. Physik, A277(1976), 299;A279(1976), 145[7] 贺泽君,李盘林,高能物理与核物理,4(1980), 640.[8] W. Pauli, FeataGhrift zum 60. Gebnrtatage A. Sommerfelds, Hirzel, Leipzig (1928), p. 30[9] M.G. Mustafa,, U. Mose1 and H. W. achmitt, Phys. Rev., C7(1973), 1519.[10] R.Kubo, K. Matano and K. Kitahara, J. Stat. Phys., 9(1973), 51.[11] M. Suzuki, Prog. Theor. Phys., 56(1976), 77.[12] R. Schmidt and G. Wolachin, Z. Phyaik A296 (1980), 215.[13] 王竹溪,统计物理学导论,人民教育出版社,第二版,北京,1978年,239页.[14] P. Fong, Phys. Rev., C10(1974), 1122.[15] U. Brosa, Z. Physik, A298(1980), 77.[16] 王正行,于相杰,黄森,《铀怀中子裂变质量分布的一个经验公式》,北京大学内部报告,1977.
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WANG CHENG-SHING. NON-EQUILIBRIUM STATISTICAL THEORY OF NUCLEAR FISSION MASS DISTRIBUTION[J]. Chinese Physics C, 1982, 6(2): 219-230.
WANG CHENG-SHING. NON-EQUILIBRIUM STATISTICAL THEORY OF NUCLEAR FISSION MASS DISTRIBUTION[J]. Chinese Physics C, 1982, 6(2): 219-230. shu
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Received: 1981-06-09
Revised: 1900-01-01
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NON-EQUILIBRIUM STATISTICAL THEORY OF NUCLEAR FISSION MASS DISTRIBUTION

  • Department of Technical Physics, Peking University

Abstract: We consider the fission process from saddle point to scission point as a non-equili-brium transport process obeying the Master equation, which can be reduced into theform of Fokker-Planck equation approximately. Taking the mass asymmetry coordinatex as the macrovariable, the nuclear fission can be considered as a diffusion process inx space, the drift velocity v(x,t), which is a non-linear. function of x, is proportionalto the gradient of the potential surface of fission nucleus in x space. The kinetics ofnuclear deformation from saddle point to scission point is represented by the variationof v(x,t) with time t phenomenologically. Assuming the mass distribution at saddlepoint is a symmetric one, and to solve the Fokker-Planck equation by means of Su-zuki's scaling limit approximation method, we get a solution which becomes a double-Gaussian asymmetric distribution on the potential valley after a time interval longenough, the width of mass distribution is proportional to nuclear temperature and in-versely proportional to relative depth of the potential valley. In the case of 235U(n,f),the time interval evaluated from saddle point to scission point would be larger than1.6×10-21 second, while it has arrived at the statistical equilibrium state. The Fong'sstatistical theory of nuclear fission is proved to be the case of stationary solution of theFokker-Planck equation exactly.

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