We propose new types of density dependent contact pairing interaction which reproduce the pairing gaps in symmetric and neutron matters obtained by a microscopic treatment of the realistic nucleon-nucleon interaction. The BCS-BEC crossover of neutrons pairs in symmetric and asymmetric nuclear matters is studied by using these contact interactions. It is shown that the bare and screened pairing interactions lead to different features of the BCS-BEC crossover in symmetric nuclear matter. We perform Hartree-Fock-Bogoliubov (HFB) calculations for semi-magic Calcium, Nickel, Tin and Lead isotopes using these density-dependent pairing interactions. It is pointed out that the isospin dependent pairing interaction reproduces well the neutron number dependence of experimental data for the binding energy, two neutrons separation energy, and odd-even mass staggering of these isotopes.