For collisions between deformed and oriented nuclei, the fragmentation theory is extended for the generalized nuclear proximity potential, with deformations included up to the hexadecupole deformations. For co-planar nuclei, the orientations are shown to get optimized (uniquely fixed) by the signs of their quadrupole deformations alone, not affected by the signs of their hexadecupole deformations. The optimum orientations are obtained for both the ‘hot compact’, and ‘cold elongated’ configurations of any two colliding nuclei. The hexadecupole deformations are shown to help fusion (hot or cold), depending on the choice of the reaction partners. Calculations are made for the 208Pb- and 48Ca-induced reactions and the neighbouring deformed nuclei. The calculated fragmentation potentials for optimally oriented nuclei, compared with both nuclei taken spherical, show that the excitation energy of the potential energy minima is significantly lowered for cold (elongated) fusion of deformed nuclei, but it remains nearly the same for at least the asymmetric hot (compact) fusion reactions. A number of new minima (target–projectile combinations) arise due to the cold and nearly symmetric hot fusion of deformed, optimally oriented nuclei.

The "pocket formula" for the proximity potential is generalized for collisions of any two (equal or unequal) deformed nuclei, having any degree of (equal or unequal) orientations (from 0°to 180°) in space. The method is applied to axially symmetric coplaner nuclei. The case of noncoplaner nuclei will be dealt with in a separate publication.

Based on fragmentation theory extended to include the orientation degrees of freedom and higher multipole deformations up to hexadecapole deformations, the compactness of 48 Ca induced reactions on various actinides is studied for Ds (Z = 110) to 118 nuclei. It is shown that the reactions leading to Z 114 nuclei are "compact" hot fusion reactions at θ = 90 • 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 θ < 90 • (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 Ca beam and to Pb based reactions. Furthermore, for compact hot fusion reactions, in addition to the 48 Ca reaction valley, a number of other new reaction valleys (target-projectile combinations) are obtained, the most important one (next to 48 Ca) being the 54 Ti nucleus used previously in Pb based cold fusion reaction studies but now proposed with deformed actinide nuclei such as 226 Ra, 232 Th, 238 U, and 242 Pu.