Mass-number dependence of statistical model parameters and its impact on incomplete fusion fraction calculations

Abstract

Incomplete fusion processes and estimation of strength of incomplete fusion in heavy ion induced nuclear reactions have been explored for several combinations of projectile-target nuclei. Dynamics of these reactions is explained using an optical model. Parameters of the optical model affect the shape and depth of nuclear potential and hence influence the theoretical predictions. For heavy ion induced reactions, the optical model potential parameters are not unique and different sets of these parameters may be used for different ranges of mass number $A$ and incident energy $E$. To explore the effect of optical model potential parameters, a comparative study of available experimental data for excitation functions of four systems, ${}^{16}\mathrm{O}+{}^{181}\mathrm{Ta}, {}^{12}\mathrm{C}+{}^{165}\mathrm{Ho}, {}^{14}\mathrm{N}+{}^{163}\mathrm{Dy}$, and ${}^{16}\mathrm{O}+{}^{74}\mathrm{Ge}$, with corresponding theoretically predicted excitation functions, made by PACE4 using different sets of optical model potential parameters, has been done. It has been observed that a single set of optical model potential parameters is not adequate for all the systems. The variations in these parameters change the theoretical cross-section predictions for various channels considerably, which in turn, change the correspondingly estimated fraction of incomplete fusion $\left(F_{\mathrm{ICF}}\right)$. The effect of deformation of target nuclei on fractional incomplete fusion has also been investigated for the above mentioned systems. $F_{\mathrm{ICF}}$ has been plotted as a function of deformation parameter $\left({\beta }_2\right)$ of the target nuclei and it is found to increase as the deformation parameter of the corresponding target nuclei increases on either side of the intrinsic spherical symmetry.