Using different types of proximity potentials, we have examined the trend of variations of barrier characteristics (barrier height and its position) as well as fusion cross sections for 50 isotopic systems including various collisions of C, O, Mg, Si, S, Ca, Ar, Ti and Ni nuclei with 1 ≤ N/Z < 1.6 condition for compound systems. The results of our studies reveal that the relationships between increase of barrier positions and decrease of barrier heights are both linear with increase of N/Z ratio. Moreover, fusion cross sections also enhance linearly with increase of this ratio.

The behaviors of barrier characteristics and fusion cross sections are analyzed by changing neutron over wide range of colliding systems. For this purpose, we have extended our previous study (Eur. Phys. J. A 48, 21 (2012), it is devoted to the colliding systems with neutron-rich nuclei) to 125 isotopic systems with condition of 0.5 ≤ N/Z ≤ 1.6 for their compound nuclei. The AW 95, Bass 80, Denisov DP and Prox. 2010 potentials are used to calculate the nuclear part of interacting potential. The obtained results show that the trend of barrier heights V B and positions R B as well as nuclear V N and Coulomb V C potentials (at R = R B ) as a function of (N/Z − 1) quantity are non-linear (second-order) whereas the fusion cross sections follow a linear-dependence. 25.60.Pj, 25.70.Jj

The recent measured values of the fusion excitation functions of the heavy-ion colliding systems 28 Si+ 100 Mo, 58 Ni+ 54 Fe, and 64 Ni+ 64 Ni are investigated using the original version of the proximity formalism. The fusion cross sections are calculated based on the coupled-channels approach, including couplings to the low-lying 2 + and 3 − states in both target and projectile nuclei. The comparison between the calculated and the measured values of the fusion excitation functions indicates that the potential Prox.77 needs to be modified considerably at sub-barrier energies. In the present study, the role of the surface energy coefficient γ and also the temperature T of the compound nucleus in nuclear potential and fusion cross section has been explored for our colliding systems. Moreover, the mutual and the multiphonon excitations of the lowest 2 + and 3 − states are considered in the coupled-channels calculations. It is demonstrated that the potential Prox.77 with these corrective effects can reproduce the experimental data of the fusion cross section, the S factor and the logarithmic derivative for fusion reactions 28 Si+ 100 Mo, 58 Ni+ 54 Fe, and 64 Ni+ 64 Ni with good accuracy especially at below-barrier energies.

The sub-barrier fusion data of 32,34S + 89Y colliding systems are analyzed using the coupled-channels (CC) calculations, including couplings to the low-lying 2+ and 3− states in reacting nuclei as well as mutual and multi-phonon excitations of these states, based on the proximity potential model. In this scheme, we focus upon the the effect of surface energy coefficient γ and also thermal properties of liquids and hot nuclei on the inner part of the nuclear potential and thus on the fusion cross sections at bombarding energies far below the Coulomb barrier. As expected, our primary calculations using the original proximity potential 1977 show that this model underestimates the measured fusion cross sections at the whole energy region. It is shown that the mentioned physical effects bring significant cross sections enhancements for both reactions. The indications of the fusion hindrance phenomenon in the fusion cross sections at energies far below the Coulomb barrier show up. The observed S factors for the above-mentioned systems develop a maximum at low energies which can also be predicted by the phenomenological extrapolations. Our results within the framework of the modified form of the proximity potential reveal that the calculated fusion cross sections, S factors, and logarithmic slopes for the two systems are in good agreement with the corresponding experimental data even at the lowest energies.

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