The first explanation on the properties of the nuclear force came from Yukawa. It said that interaction between two nucleons is mediated by mesons (heavy bosons). The most effective practical model for a quantitative nucleon-nucleon potential has been meson-exchange theory ever since. Manning-Rosen potential (M-R pot) is a diatomic molecular potential but in the moderate range it behaves as the Yukawa potential. Thus M-R pot can be considerable for the nuclear domain also. We have treated both the on- and off-shell two-particle nuclear scattering in the non-relativistic region.