**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 R^{2}, 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}**