Assume that each nucleon inside a stable nucleus interacts attractively only with a fixed number of nearest neighbours due to the short–range and saturation properties of the nuclear force.
(i) If the average binding contribution of one such nucleon–nucleon pair is ε0, show that the total binding energy EB of a nucleus containing A nucleons can be written approximately as EB≈αA, where α is a constant to be expressed in terms of ε0 and the average number of interacting pairs per nucleon.
(ii) Hence deduce that the binding energy per nucleon Eˉ=EB/A is nearly constant for a wide range of nuclei.
(iii) Discuss briefly why very light nuclei (small A) and very heavy nuclei (large A) deviate from this constancy, referring to surface effects and Coulomb repulsion respectively.