The nuclear surface tension coefficient, , of the proximity potential is systematically investigated from the microscopic double-folding (DF) model accompanied by the realistic density-dependent nucleon–nucleon (NN) interactions. In the present work, we select six versions of density-dependent M3Y–Paris effective NN forces, including DDM3Y1 (with K=176), CDM3Y1 (with K=188 MeV), CDM3Y3 (with K=217 MeV), CDM3Y5 (with K=241 MeV), CDM3Y6 (with K=252 MeV) and BDM3Y1 (with K=270 MeV). A total of 70 heavy-ion fusion reactions with condition for the charge product of their reacting nuclei have been analyzed. By fitting the calculated values against the asymmetry parameter , we present a new analytical formula for the parameter which is directly dependent on the nuclear matter (NM) incompressibility constant . It is shown that the presently obtained formula in proximity potential model can reproduce the fusion data well. In this study, a discussion is also presented about the influence of the incompressibility constant on the interaction potentials and also on the fusion cross sections resulting from the proximity approach for different heavy-ion reactions.
