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NUCLEI Theory

Cluster Aspects of Binary and Ternary Fission* A. V. Andreev1), 2)** , G. G. Adamian1), 3) , N. V. Antonenko1), 2) , S. P. Ivanova1) , S. N. Kuklin1), and W. Scheid2) Received October 31, 2006

Abstract—On the basis of the statistical approach and calculation of the potential energy of the scission configurations, binary and ternary fissions are described. PACS numbers: 24.75.+i, 21.60.Gx DOI: 10.1134/S1063778807090268

1. BIMODALITY IN FISSION OF ACTINIDES The experiments [1–3] revealed interesting spontaneous fission properties of the nuclei 258,259 Fm, 259,260 Md, and 258,262 No in which the total kinetic energy (TKE) distributions of the fragments appeared to be composed of two Gaussians with the maxima near 200 and 230 MeV. It was found that the high TKE is associated with a narrow symmetrical mass distribution, while the low-energy fragments produce a broad symmetrical and, in some cases, an asymmetrical mass distribution. It appears that each distribution arises from a separate mode of fission, and this phenomenon is called bimodal fission. In the present work, the fissioning nucleus with mass A and charge Z can be described at the scission point as a dinuclear system (DNS) with the two fission fragments in contact with the mass and charge numbers Ai and Zi (i = 1, 2). The DNS fragments are modeled by nearly touching, coaxial prolate ellipsoids. The deformation parameters βi are defined as the ratios of the major and minor axes of the ellipsoids.

where d is the distance between the centers of the fragments, UiLD the liquid-drop part of the energy of the ith fragment, and V C and V N are the Coulomb and nuclear [4] interaction potentials, respectively. The shell correction Uish is calculated according to the Strutinsky prescription [5] by using the two-center shell model [6]. The rotational energy V rot is calculated by assuming the rigid-body moments of inertia. For spontaneous fission, V rot = 0. The details of the potential energy calculations are given in [7]. For two given fragments, the interaction potential V C + V N as a function of the distance d has a small potential pocket and a barrier at a distance d = dbarr close to the scission point [4, 7]. In order to compare the yields of different configurations, one should use the values of the potential energy corresponding to this barrier. In order to calculate the relative primary (before evaporation of neutrons) yields Y of fission fragments, we use the following expression [8]: Y ({Ai , Zi , βi })

The potential energy of the scission configuration is calculated from the expression U ({Ai , Zi , βi }, d, L) = U1LD (A1 , Z1 , β1 )

+ ∗

(1)

+ δU1sh (A1 , Z1 , β1 ) + U2LD (A2 , Z2 , β2 ) + δU2sh (A2 , Z2 , β2 ) + V C ({Ai , Zi , βi }, d) V N ({Ai , Zi , βi }, d) + V rot ({Ai , Zi , βi }, d, L),

The text was submitted by the authors in English. Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980 Russia. 2) ¨ Institut fur Theoretische Physik der Justus-Liebig¨ Giessen, Germany. Universitat, 3) Institute of Nuclear Physics, Tashkent, Uzbe