Influence of shell effects on mass asymmetry in fission of different Hg isotopes

With the improved scission-point model mass distributions are calculated for induced fission of Hg isotopes with even mass numbers A = 174 – 198. The calculated mass distributions and mean total kinetic energy of fission fragments are in good agreement with the existing experimental data. The asymmetric mass distribution of fission fragments of 180Hg observed in the recent experiment is explained. The change in the shape of the mass distribution with increasing A of the fissioning Hg nucleus from symmetric for 174Hg to asymmetric around 180Hg, and to more symmetric for 192−198Hg is revealed. The interest to the theoretical exploration of fission process was re-stimulated several years ago after the experiment on -delayed fission of 180Tl [1, 2], where the mass distribution of fission fragments in the fission of the post-decay daughter nucleus 180Hg was found to be strongly asymmetric. That was surprising since from the previous investigations the mass distributions were expected to be symmetric for the nuclei lighter than thorium. Some indications of slight asymmetry were observed earlier in the experiments on fission of Au-Po nuclei [3], but the difference of the mass distribution shape from symmetric Gaussian shape was rather small. The experiment [1] was followed by several theoretical works describing the observed asymmetric shape of the fission-fragment mass distribution [4–7]. The present work is the extension of our previous calculations [4] to the wider range of Hg isotopes in order to explore the fission fragment mass distribution shape dependence on the mass number A of the fissioning Hg isotope and compare with the results of other theoretical models. We describe the nuclear fission observables within the improved scission-point model [4, 8] which operates with relative probabilities of formation of different scission configurations obtained with statistical approach by calculating the potential energy of scission configurations. The fissioning nucleus at the scission point is modeled by a dinuclear system consisting of two nearly touching prolate coaxial spheroids with deformation parameters defined as the ratios of the major and minor semi-axes of the spheroids i = ci/ai , where i = L,H denotes light and heavy fragments of the dinuclear system, respectively. The mass and charge numbers of the fragments are Ai and Zi , respectively. A = AL + AH and Z = ZL + ZH are the mass and charge numbers of the fissioning nucleus, respectively. The potential energy (1) of the dinuclear system consists of the energies of the fragments, energy of their interaction, and rotational energy V rot in case of induced fission. The energy of each fragment consist of the liquid-drop energy U i , deformation dependent shell correction term U shell i , and the energy of This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20136206007 EPJ Web of Conferences the zero-point vibrations U i , associated with the energy E 2+ of the first 2+ excited state. The damping of the shell corrections with temperature is introduced in order to take into account the influence of the excitation energy. The interaction potential consists of the Coulomb interaction potential V C of the two uniformly charged spheroids and nuclear interaction potential V N in the form of a double folding of Woods-Saxon nuclear densities of the fragments and Skyrme-type density-dependent nucleon-nucleon interaction. The interaction potential has a pocket at a distance between the tips of the fragments of about 0.5-1 fm (in the considered region of fissioning nuclei) depending on deformations of the fragments. The internuclear distance R is taken corresponding to the position of this pocket (minimum) R = Rm( i). The excitation energy E∗ is calculated as the initial excitation energy of the fissioning nucleus plus the difference between the potential energy of the fissioning nucleus and the dinuclear system at the scission point. The details of the calculations of the potential energy can be found in [4]. U (Ai ,Zi , i ,R, l) = U L (AL,ZL, L)+ U L (AL,ZL, L)+ U L (AL,ZL) +ULD H (AH ,ZH , H )+ U H (AH ,ZH , H )+ U H (AH ,ZH ) +V (Ai ,Zi , i ,R)+ V N (Ai ,Zi , i ,R)+ V rot (Ai ,Zi , i ,R, l), (1) R = Rm(Ai ,Zi , i , l). The relative probability of formation of a dinuclear system with particular masses, charges and deformations of the fragments is calculated within the statistical approach as follows: Y (Ai ,Zi , i , l) ∼ exp { − (Ai ,Zi , i , l) T (l) } · (2) The temperature is T (l) = √E∗(l)/a, where a = A/12 is the level density parameter. In order to obtain the mass distribution in fission of a particular nucleus with the mass number A and charge number Z one should integrate (2) over ZL, L, and H , sum over l, and take into account that AL + AH = A and ZL + ZH = Z. Finally, for the calculation of mass distribution the following expression is obtained: