Eur. Phys. J. A (2014) 50: 152
https://doi.org/10.1140/epja/i2014-14152-4

Regular Article - Theoretical Physics

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

¹ Kalinganagar (K8/636), 751003, Bhubaneswar, India
² Department of Physics, North Orissa University, 757003, Baripada, India

^* e-mail: bd_sahu@yahoo.com

Received: 18 May 2014
Revised: 3 September 2014
Accepted: 14 September 2014
Published online: 16 October 2014

Abstract

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.