The variances of the mass distribution of fission fragments for nuclei in the fissility parameter range 30

A model is developed which combines dynamical (Langevin-) calculations with the Kramers modified statistical model in order to describe heavy-ion induced fission including neutron evaporation. In the example of the 19F + 181Ta collision, the energy dependence of fission probabilities, neutron multiplicities and (H.I., xn)-cross sections is calculated and a fair agreement with the data is achieved with a reduced friction parameter of fl = 3* 102~sec-1 We pay particular attention to the angular momentum dependence of the fusion-fission process. PACS: 25.70.Gh; 25.70.Jj The use of a transport equation to describe the fission process was pioneered by Kramers [1]. The emission of neutrons in the framework of a Fokker-Planck description of fission was investigated in a series of papers by Grange etal., see e.g. [2]. See in the respect also work by Zhuo et al. [3] and references therein. An extension to a temperature dependent potential was made in [4] where also the importance of proton and alpha particle emission is stressed. Abe etal.[5] have suggested an alternative description of the fission process in terms of Langevin equations, which have also been shown to be a useful tool in the description of deepinelastic collisions and fusion [6][7][8]. In [9] it has been shown that a Langevin procedure yields results in agreement with the propagator method [10] to solve the Fokker-Planck equation. Gonchar et al. [11] have also applied Langevin dynamics to nuclear fission. In all of these papers Langevin trajectories are not followed to very long times in cases where they enter the pocket of the potential. It is here that a new aspect is entered in the present work as compared to the related work discussed above. Because one cannot follow Langevin trajectories for arbitrary long times, we propose to follow * Also Fachbereich Physik, Freie Universitfit Berlin ** Permanent address: Railway Engineering Institute, Omsk, Russia the trajectories only until a certain delay time te beyond which one enters the validity regime of the statistical model. As is described in detail below, this procedure combines dynamical Langevin calculations with the statistical model and allows us to calculate the energy dependence of fission probabilities, neutron multiplicities and (H.I.,xn)-cross sections simultaneously.Any model of the fusion-fission process of heavy ions needs information on the formation probability of the compound system as a function of the angular momentum. Because there is a rapid change in the fission probability in the angular momentum region where the fission barrier crosses the neutron binding energy, a sensitivity to the spin distribution of the fused system is expected. In the literature [12][13][14][15] the fusion cross section is often parametrized as(1)The quantity lc is sometimes obtained from a model and the diffuseness 61 is used as a fitting parameter. Because there is very conflicting information on the values for 6l in the literature [12-15], we do not parametrize the spin distribution by fitting some data...

The variance 0 .2 of the fission-fragment kinetic-energy distribution is calculated in Ek describing the dynamics of fission of an excited nucleus by a Fokker-Planck equation for the quantum distribution function of two collective coordinates (the distance between the centers of mass of the nascent fragments and the neck parameter) and their conjugate momenta. In the calculations fluctuations in collective coordinates near scission and prescission kinetic energy have been taken into account simultaneously. The results of statistical model calculations for the case of high friction in fission mode and those of the calculations in the framework of a dynamical model for zero nuclear viscosity are the limiting cases of the proposed model. The dependence of a2 upon the fissility parameter is studied.

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