text: The term  is known as the pairing term (possibly also known as the pairwise interaction). This term captures the effect of spin coupling. It is given by
  where  is found empirically to have a value of about 1000 keV, slowly decreasing with mass number A. The binding energy may be increased by converting one of the odd protons or neutrons into a neutron or proton, so the odd nucleon can form a pair with its odd neighbour forming and even Z, N. The pair have overlapping wave functions and sit very close together with a bond stronger than any other configuration. When the pairing term is substituted into the binding energy equation, for even Z, N, the pairing term adds binding energy, and for odd Z, N the pairing term removes binding energy.
  The dependence on mass number is commonly parametrized as
  The value of the exponent k is determined from experimental binding-energy data. In the past its value was often assumed to be −3/4, but modern experimental data indicate that a value of −1/2 is nearer the mark:
  :  or 
  Due to the Pauli exclusion principle the nucleus would have a lower energy if the number of protons with spin up were equal to the number of protons with spin down. This is also true for neutrons. Only if both Z and N are even, can both protons and neutrons have equal numbers of spin-up and spin-down particles. This is a similar effect to the asymmetry term.
  The factor  is not easily explained theoretically. The Fermi-ball calculation we have used above, based on the liquid-drop model but neglecting interactions, will give an  dependence, as in the asymmetry term. This means that the actual effect for large nuclei will be larger than expected by that model. This should be explained by the interactions between nucleons. For example, in the shell model, two protons with the same quantum numbers (other than spin) will have completely overlapping wavefunctions and will thus have greater strong interaction between them and stronger binding energy. This makes it energetically favourable (i.e. having lower energy) for protons to form pairs of opposite spin. The same is true for neutrons.