Effect of compact and elongated configurations on the spontaneous and induced fission of Fm isotopes

Abstract

The spontaneous fission (SF) analysis of even mass $^{242\ensuremath{-}260}\mathrm{Fm}$ isotopes is carried out using a preformed cluster model based on quantum mechanical fragmentation theory. The deformation effects are included up to the quadrupole (${\ensuremath{\beta}}_{2}$) deformed nuclei with optimum orientations (${\ensuremath{\theta}}_{i}^{\mathrm{opt}.}$) leading to hot-compact (side-to-side) and cold-elongated (tip-to-tip) configurations. The spherical and hot-compact deformed configurations of decay fragments result in the symmetric fragment mass distributions for Fm isotopes; however, the symmetric peak gets sharper with an increase in the neutron ($N$) number of the parent nucleus. In the case of cold orientations, a transition from two-peaked (asymmetric fission) to three-peaked (multimodal fission) mass distribution is observed with an increase in the mass number of Fm. The SF half-lives (${T}_{1/2}^{\mathrm{SF}}$) are calculated using the neck-length parameter ($\mathrm{\ensuremath{\Delta}}R$) for $^{242\ensuremath{-}260}\mathrm{Fm}$ isotopes and compared with the experimental data. Besides this, the induced fission of Fm isotopes is studied within the dynamical cluster-decay model. The energy dependence of fission fragment mass distributions and the isotopic dependence is analyzed at energy range ${E}^{*}=5$--42 MeV. In addition, the role of temperature-dependent deformations in the fission dynamics is also explored.