Fusion dynamics of spherical and deformed projectiles with hexadecapole deformed target nuclei

Abstract

The quadrupole ($\beta _{\lambda =2}$) deformation and corresponding cold and hot optimum orientations of the nuclei play an important role in the synthesis of new nuclear entity. Consequently, a comprehensive knowledge is required to understand the relevance of higher-order deformed nuclei in the nuclear fusion dynamics. In the present work, the hexadecapole ($\beta _{\lambda =2,4}$) deformed nuclei of different shapes, i.e. $\beta _2^+\beta _4^+$ ($^{147-150,152,154}$Sm), $\beta _2^+\beta _4^-$ ($^{172,174,176,178,180,182}$Yb), $\beta _2^-\beta _4^+$ ($^{40,43,55,77,82}$Sc) and $\beta _2^-\beta _4^-$ ($^{70,72-74}$Ge) are taken into consideration as target of $^{16}$O (sph.), $^{48}$Ca (sph.), $^{48}$Ar ($\beta _2^-$) and $^{62}$Fe ($\beta _2^+$) induced reactions. For these selected choices of projectile-target (p-t) combinations, the impact of ± signs and hot/cold optimum orientations of higher-order deformation (up to $\beta _4$) has been investigated, in reference to that $\beta _2^{\pm }$ deformation. The above analysis has been discussed in terms of fusion barrier characteristics (barrier height $V_B$ and barrier position $R_B$), which is sensitive towards the deformation and orientation degree of freedom. Furthermore, the corresponding effects have been analyzed in the calculation of fusion cross-section $\sigma _{fus}$, with respect to the center of mass energy ($E_{c.m.}$) lying across the Coulomb barrier. Therefore, the nuclear shape for targets $\beta _2^{\pm }\beta _4^+$ expands relatively larger, and consequently the radius which enhances the fusion cross-sectional area as compared to that of $\beta _2^{\pm }$ deformation. In contrast to the above case, the $\beta _2^{\pm }\beta _4^-$ shapes have been found to hinder the fusion, mainly at the below- and near-barrier regions. Subsequently, the present work gives the relevance of the expanded and compressed shapes of hexadecapole deformed nuclei in the nuclear fusion dynamics for the considered choices of p-t combinations at the low-energy regime. Besides, the available experimental data for $^{16}$O+$^{147-150,152,154}$Sm p-t combinations, here ‘Sm’ isotopes are $\beta _4^+$-deformed, has been addressed by integrating $\sigma _{fus}$ over all orientations and deformations up to $\beta _4$, over a given range of $E_{c.m.}$.