Theoretical study of odd-mass Fr isotopes using the collective clusterization approach of the dynamical cluster-decay model

Abstract

The reaction dynamics of various odd-mass Fr isotopes is studied over a wide range of incident energies, spread across the Coulomb barrier. The specific reactions analyzed are ${}^{18}$O+${}^{197}$Au and ${}^{19}$F+${}^{192,194,196,198,200}$Pt, forming odd-mass ${}^{211\ensuremath{-}219}$Fr${}^{*}$ compound systems where some data are available for three of these isotopes: ${}^{213,215,217}$Fr${}^{*}$. Based on the dynamical cluster-decay model (DCM), we have extended our calculations of the evaporation residue (ER) cross sections to the mainly fissioning ${}^{215}$Fr${}^{*}$, using the systematics of ${}^{213,217}$Fr${}^{*}$ isotopes where the available ER cross sections (as well as fusion-fission cross sections) were studied earlier within the DCM. In order to obtain a clear picture of the dynamics involved, including entrance channel effects, the variations of fragmentation potential, preformation factor, and decay barrier height are analyzed. The relevance of barrier modification effects is also explored in the decay of ${}^{213,215,217}$Fr${}^{*}$ nuclei. In addition, fusion-fission (ff) cross sections are extended to ${}^{213,217}$Fr${}^{*}$ systems where some more data has recently become available. Also, the fission fragment anisotropies (so far measured and studied for ${}^{215}$Fr${}^{*}$ alone) are estimated for ${}^{213,217}$Fr${}^{*}$ using DCM for the use of nonsticking moment of inertia, and relevant comparison with the sticking moment-of-inertia approach is analyzed. Furthermore, the shell closure effects of the decay fragments are investigated for odd-mass ${}^{211\ensuremath{-}219}$Fr${}^{*}$ isotopes.