Combining a langevin description of heavy-ion induced fission including neutron evaporation with the statistical model

Abstract

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...

Fission process of nuclei at low excitation energies with a Langevin approach

“…Actually, a complete Langevin description of the fission process must also consider the evaporation of light particles and switches over to the statistical model description when the fission process reaches the stationary regime [40]. This method can be used to treat all decay processes.…”

Dynamical treatment of fission fragment angular distribution

“…The evaporation of prescission light particles (j = n, p, α, γ ) along Langevin trajectories was taken into account using a Monte Carlo simulation technique [15,26]. All the dimensional factors were recalculated when a light prescission particle was evaporated, only the dimensionless functionals of the rotational, Coulomb and nuclear energies were not recalculated.…”

Role of dynamical deformation in pre-scission neutron multiplicity

“…Here, M R (M CN ) is the mass of the daughter nucleus (CN), M ν is the mass of the emitted particle, and D R (c) (D CN (c)) denotes the deformation energy of the daughter nucleus (CN) at a particular deformation c. In the present work, experimental masses (M R and M CN ) are used to calculate B ν (c). Usually, dynamical calculations are often combined with a subsequent statistical model calculation [26,32,[45][46][47] due to computational limitations. Nevertheless, the motivation in this work is to distinguish the deformation of a CN for each of the particle and γ decay.…”

“…During the dynamical evolution, neutron (n), proton (p), α-particle, and γ-ray evaporations are considered within the Monte-Carlo method of random sampling [32]. The corresponding decay widths are evaluated at each time step with appropriate incorporation of its variation with nuclear deformation.…”