Semi-empirical Mass Formula

Carl F. von Weizsacher, 1930's

Assume that nucleus is a collection of interacting particles in the form of a liquid drop.

Semi-empirical ®  the numerical values

Binding energy = Volume term + Surface term + Coulomb term + Symmetry term + Pairing term

a_V = 14 MeV        Binding energy is approximately the sum of all interactions between nucleons due to short range nature of nuclear force.

a_A = 13 MeV        Surface nucleons do not have saturated interactions.  Contribution proportional to R², hence A^2/3 dependence.  

Coulomb term         Change in energy due to adding a charge dq to a solid sphere of radius r.  Self energy is subtracted, yielding Z(Z-1) dependence.

a_S = 19 MeV        Without Coulomb force, binding energy is a minimum for Z = N.  Note that (N-Z)² >0

pairing d =  +D  for even-even
                     0  for odd
                   -D for odd-odd

D = 33MeV*A^-3/4