Coulomb-nuclear potential resonances for oscillatory structure in second energy derivative of fusion cross section times energy

摘要

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 σR in the presence of such resonances and present them in the form of a quantity D_F(E) = (d~2 (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 ?. Hence each ? 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 ?s 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 σF at different energies in the cases of heavy-ion system of reactions, namely ~(16)O+~(208)Pb, ~(36)S+ ~(110)Pd, ~(58)Ni + ~(60)Ni and thereby it is confirmed that peaks and dips found in the variation of D_F(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.