New Approach to Description of Fusion-fission Dynamics in Super-heavy Element Formation

Abstract

A new mechanism of the fusion-fission process for a heavy nuclear system is proposed, which takes place in the (A1, A2) space, where A1 and A2 are two nuclei, surrounded by a certain number of shared nucleons ∆A. The nuclei A1 and A2 gradually lose (or acquire) their individualities with increasing (or decreasing) a number of collectivized nucleons ∆A. The driving potential in the (A1, A2) space is derived, which allows the calculation of both the probability of the compound nucleus formation and the mass distribution of fission and quasi-fission fragments in heavy ion fusion reactions. The cross sections of super-heavy element formation in the “hot” and “cold” fusion reactions have been calculated up to ZCN = 118. The interest in the synthesis of super-heavy nuclei has lately grown due to the new experimental results 1, 2 demonstrating a real possibility of producing and investigating the nuclei in the region of the so-called “island of stability”. The new reality demands a more substantial theoretical support of these expensive experiments which will allow a more reasonable choice of fusing nuclei and collision energies as well as a better estimation of the cross sections and unambiguous identification of evaporation residues (ER). Unfortunately, at present it is quite difficult (and hardly possible) to make an accurate qualitative analysis of the complex dynamics of the heavy ion fusion reaction leading to the formation in the exit channel of ER of easily fissile super-heavy nucleus. A whole process of super-heavy nucleus formation is divided usually into three reaction stages even if connected with each other but treated and calculated separately: (1) overcoming the Coulomb barrier and approaching the point of contact Rcont = R1 + R2, (2) formation of the compound mono-nucleus, (3) decay (“cooling”) of the compound nucleus. Different theoretical approaches are used for analyzing all the three reaction stages. However, the dynamics of the intermediate stage of the compound nucleus formation is the most vague. It is due to the fact that in the fusion of light and medium nuclei, in which the fissility of the compound nucleus is not very high, the colliding nuclei having overcome the Coulomb barrier form a compound nucleus with a probability PCN ≈ 1. Thus, this reaction stage does not influence the yield of ER at all. However, in the fusion of heavy nuclei it is the fission channels (regular and quasifission) that substantially determine the dynamics of the whole process; the PCN value can be much smaller than unit, while its accurate calculation is very difficult. Moreover, today there are no consensus for the mechanism of the compound nucleus formation itself, and quite different, sometimes opposite in their physics sense, models are used for its description. 3‐5 The production cross section of a cold residual nucleus C, which is the product of neutron evaporation and γ emission from an excited compound nucleus C ∗ , formed in the fusion process of two heavy nuclei A1 + A2 → C ∗ → C+ xn+ Nγ at center-ofmass energy close to the Coulomb barrier in the entrance channel, can be decomposed over partial waves and written in the following form σ xn(E) ≈ π¯ h 2 2µE