Coulomb-nuclear potential resonances for oscillatory structure in second energy derivative of fusion cross section times energy
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In a nucleus-nucleus collision, resonances depicted by larger values of reaction cross section (σ R) 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 (σ F) from σ R in the presence of such resonances and present them in the form of a quantity D F(E) = (d2(Eσ F)/dE 2): the second energy derivative of the product of σ F and energy E. In principle the variation of the quantity D F(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 D F(E) over a range of energy. These results of D F(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 D F(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 D F(E) give successful explanation of the corresponding results extracted from the experimental results of σ F 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 D F(E) extracted from the measured results of σ F as a function of the energy are critically influenced by the potential pocket resonances generated in the reactions.
KeywordsPartial Wave Reaction Cross Section Fusion Cross Section Lower Energy Region 208Pb System