Consistent application of the finite-range liquid-drop model to Langevin fission dynamics of hot rotating nuclei

Abstract

A generalized finite-range liquid-drop model based on the Yukawa-plusexponential potential was applied to describe fission dynamics of hot rotating nuclei. The potential energy, level-density parameter and Helmholtz free energy are calculated in a consistent way by using the generalized finiterange liquid-drop model. The level-density parameter was approximated by a leptodermous-type expression. The coefficients of this expansion are in surprisingly good agreement with those obtained earlier by Ignatyuk and co-workers. The results of Langevin dynamical calculations of the mean prescission neutron multiplicity and fission probability are practically the same both for the level-density parameter calculated with Ignatyuk's coefficients and the one calculated using the generalized finite-range liquid-drop model. This fact lets us assume that all previous results of dynamical Langevin calculations performed with Ignatyuk's level-density parameter stay reliable.

Dynamical treatment of fission fragment angular distribution

“…The temperature of the heat bath T has been determined by the Fermi-gas formula T = (E int /a(q)) 1/2 , where E int is the internal excitation energy of the nucleus and a(q) is the level-density parameter, which has been taken from the work of Ignatyuk et al [16]. It should be noted that the asymptotic level-density parameter obtained by Ignatyuk and his co-workers is in surprisingly good agreement with the level-density parameter, calculated [17] in a consistent way by using a temperature-dependent finite-range liquid drop model [18]. The repeated indices in the equation above imply summation over the collective coordinates from 1 to 3.…”

Cross sections for the production of superheavy nuclei

“…The use of the Kramers factor allows one to match the fission rate (width) calculated by Eq. (20) and the quasistationary fission rate obtained in dynamical calculations (see, e.g., [26][27][28]). The appearance of the temperature in the denominator of Eq.…”

“…Energy, angular and mass distributions of primary reaction fragments are given by formula (28) and Eqs. (25).…”

Conditions for the manifestation of transient effects in fission

“…The deformation dependence of the level-density parameter has been discussed in references [33,34,36,35]. In our case, the ratio a f /a n is calculated considering volume and surface dependencies as proposed in reference [36] .…”

“…[37]. A recent work of Karpov et al [35] has shown that equation (44) is well adapted by comparing it to several derivations: in the framework of the liquid-drop model including a Coulomb term [38], with the finite-range liquid-drop model [39] and within the relativistic mean-field theory [40]. The angularmomentum-dependent fission barriers are taken from the finite-range liquid-drop model predictions of Sierk [41].…”