Fission barrier heights and lifetimes for heavy and superheavy nuclei

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$M. Winiarski, Prezentacje multimedialne w LATEX-u$

The parametrisations (1) and (3) which we introduced till now are restricted to axially deformed shapes. It is well known, however, that in the actinide region, non-axial shapes are favoured near the first saddle. Without attempting to describe such shapes in the fully general case, we assume that the cross section perpendicular to the z axis is an ellipse with half axes a^ and Uy which, of course, depend on z. In polar coordinates 2 2 ^^'(^'
a diffuseness correction and an exchange contribution of the N-body wavefunction. A modern version of the Liquid-Drop model is presented below. The fluctuating part 5E^^ of the nuclear energy is usually evaluated in the form ^•E'mic = ^•E'shell + ^•E'pair ' (11) where the first term, refered to as the shell-correction energy, contains that part of the fluctuation which is due to the nuclear shell structure, and where the second term is due to the pairing correlations between the nucleons. For a system like the atomic nucleus which is composed of two sorts of fermions, protons and neutrons, the calculation of shell-correction and pairing energy needs to be carried out for both types of nucleons with 8E^^^^^ and 8E^^^ getting contributions from neutrons and protons. To determine single-particle spectra of a given nucleus at a given deformation, as is needed both in the Strutinsky shell correction energy and in the BCS pairing treatment, one has to define single-particle potentials for any shape. To do that we prefer not to use the prescription of ref. [1] which defined single-particle densities and potentials as Fermi type functions perpendicular to the equivalent sharp surface, given e.g. by Eq. (9), since such a prescription does not allow for an unambiguously definition of these quantities for necked-in shapes appearing in the vicinity of the scission configuration. Neutron and proton densities as well as the corresponding single-particle potentials can, however, be unambiguously defined by folding the deformed equivalent sharp surface with an appropriate folding function [16] (see also Ref. [13] for details). The Lublin-Strasbourg Drop Model In our macroscopic-microscopic model the average nuclear binding energy is determined using the Lublin-Strasbourg-Drop (LSD) [7] as a function of mass and charge number (via the isospin parameter I) and the nuclear deformation £^,(Z,7V;def) =flvoi(l - K-vo/)^ + asur(l - K,^f)A^I^B,„,{def) + acur (1 - Kcur/2)^'''^5cur(def) + | ^ -^5coul(def) - C4 |- -£'cong , (12) where the parameters, listed in Table 1, are adjusted to all 2766 experimental binding energies taken from Ref. [17] using the microscopic corrections from [8] and the congruence energy iicong estimated according to [18]. The functions isur(def), icur(def), -5coui(def) defined as the variation, relative to the spherical shape, of the nuclear surface, curvature and Coulomb energies, can be evaluated for any nuclear shape [19] and, in particular, for the MFH shapes used in this work. It has been demonstrated that Eq. (10) v^'ithE^^^ (12) and 8E^:^^ taken from [8] is not only able to describe the experimental binding energies of all presently known nuclei with a very good accuracy [7], but experimental fission barrier heights as well [9] as pointed out above. 235
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Page 3: ensures volume conservation of the
Page 7 and 8: heights estimates of Ref [20]. Keep

Fission barrier heights and lifetimes for heavy and superheavy nuclei

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