Cold nuclear matter effects and a modified form of the proximity approach

The influence of the cold nuclear matter effects on the Coulomb barriers and also on the fusion cross sections of 47 fusion reactions are systematically investigated within the framework of the proximity formalism. For this purpose, I modify the original version of this formalism (Prox. 77) using a new analytical form of the universal function which is formulated based on the double-folding model with three density-dependent versions of the M3Y-type interactions, namely DDM3Y1, CDM3Y3 and BDM3Y1. It is found that when the Prox. 77 potential is accompanied by each of the formulated universal functions, the agreement between the theoretical and experimental data of the barrier height and also the fusion cross section increase for our selected fusion systems. The present study also provides appropriate conditions to explore theoretically the variation effects of the NM incompressibility constant $K$ on the calculated results caused by the Prox. 77 model. It is shown that the accuracy of this potential model for reproducing the experimental fusion data enhances by increasing the strength of this constant. A discussion is also presented about the role of various physical effects in the theoretical results of the proximity approach.