In a nucleus-nucleus collision, resonances depicted by larger values of reaction cross section (σR) at specific energies are generated by the combined Coulomb-nuclear potential by virtue of well-developed pocket in it. The generation of such resonance is ascertained by the peak value of phase-shift time or dwell time at the resonance energy. We extract the results of fusion cross section (σF) from σR in the presence of such resonances and present them in the form of a quantity DF(E) = (d2(EσF)/dE2): the second energy derivative of the product of σF and energy E. In principle the variation of the quantity DF(E) as a function of energy shows two peaks and a negative dip between them around each resonance energy stated above. There can be several resonances in a given angular momentum trajectory denoted by partial wave ℓ. Hence each ℓ would carry a number of peaks and dips for the result of DF(E) over a range of energy. These results of DF(E) from a large number of ℓs involved in a heavy-ion collision shall be added together and, after some mutual cancellation and/or addition, the final result of DF(E) will show an oscillatory structure with a large number of residual peaks and dips present over the range of energy of variation. These calculated results of DF(E) give successful explanation of the corresponding results extracted from the experimental results of σF at different energies in the cases of heavy-ion system of reactions, namely 16O + 208Pb, 36S + 110Pd, 58Ni + 60Ni and thereby it is confirmed that peaks and dips found in the variation of DF(E) extracted from the measured results of σF as a function of the energy are critically influenced by the potential pocket resonances generated in the reactions.
Partial Wave Reaction Cross Section Fusion Cross Section Lower Energy Region 208Pb System
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