Angular momentum effects and barrier modification in sub-barrier fusion reactions using the proximity potential in the Wong formula

Using the capture cross-section data from {sup 48}Ca+{sup 238}U, {sup 48}Ca+{sup 244}Pu, and {sup 48}Ca+{sup 248}Cm reactions in the superheavy mass region, and fusion-evaporation cross sections from {sup 58}Ni+{sup 58}Ni, {sup 64}Ni+{sup 64}Ni, and {sup 64}Ni+{sup 100}Mo reactions known for fusion hindrance phenomenon in coupled-channels calculations, the Wong formula is assessed for its angular momentum and barrier-modification effects at sub-barrier energies. The simple, l=0 barrier-based Wong formula is shown to ignore the modifications of the barrier due to its inbuilt l dependence via l summation, which is found to be adequate enough to explain the capture cross sections for all the three above-mentioned {sup 48}Ca-based reactions forming superheavy systems. For the capture (equivalently, quasifission) reactions, the complete l-summed Wong formula is shown to be the same as the dynamical cluster-decay model expression, of one of us (R.K.G.) and collaborators, with the condition of fragment preformation probability P{sub 0}{sup l}=1 for all the angular momentum l values. In the case of fusion-evaporation cross sections, however, a further modification of barriers is required for below-barrier energies, affected in terms of either the barrier 'lowering' or barrier 'narrowing' via the curvature constant. Calculations are made for use of nuclear proximity potential, with effectsmore » of multipole deformations included up to hexadecapole, and orientation degrees of freedom integrated for both the coplanar and noncoplanar configurations.« less