Compactness of theCa48induced hot fusion reactions and the magnitudes of quadrupole and hexadecapole deformations

Abstract

Based on fragmentation theory extended to include the orientation degrees of freedom and higher multipole deformations up to hexadecapole deformations, the compactness of $^{48}\mathrm{Ca}$ induced reactions on various actinides is studied for Ds ($Z=110$) to 118 nuclei. It is shown that the reactions leading to $Z\ensuremath{\ge}114$ nuclei are ``compact'' hot fusion reactions at $\ensuremath{\theta}={90}^{\ifmmode^\circ\else\textdegree\fi{}}$ orientation angles (equatorial compact or ec; collisions that are in the direction of the minor axis of the deformed reaction partner), but the ones for $Z<114$ nuclei are compact at $\ensuremath{\theta}<{90}^{\ifmmode^\circ\else\textdegree\fi{}}$ (not-equatorial compact or nec). The phenomenon of ``barrier distribution in orientation degrees of freedom'' is observed for the first time to be related to the magnitudes of both the quadrupole and hexadecapole deformations of the deformed reaction partner. The ec configurations are obtained for the cases of quadrupole deformation alone and with small (including negative values) hexadecapole deformations. The presence of large (positive) hexadecapole deformations result in the nec configurations. These results are found to be quite general, applicable also to other lighter targets such as W and Ra with the $^{48}\mathrm{Ca}$ beam and to Pb based reactions. Furthermore, for compact hot fusion reactions, in addition to the $^{48}\mathrm{Ca}$ reaction valley, a number of other new reaction valleys (target-projectile combinations) are obtained, the most important one (next to $^{48}\mathrm{Ca}$) being the $^{54}\mathrm{Ti}$ nucleus used previously in Pb based cold fusion reaction studies but now proposed with deformed actinide nuclei such as $^{226}\mathrm{Ra}$, $^{232}\mathrm{Th}$, $^{238}\mathrm{U}$, and $^{242}\mathrm{Pu}$.