A special value is used to adjust for pairing of nucleons. For odd-even
or even-odd nuclides, E_{o} = 0. For even-even nuclide,
E_{o} has a positive value and for odd-odd nuclide,
E_{o} has a negative value. This adjustment accounts
for the high stability of even-even nuclides, and low stability of
odd-odd nuclide.
Binding energy of isobars
Isobars have the same mass number A but different atomic number.
Binding energy varies with atomic number. The stable isobar ideally has
the maximum binding energy. Mathematically, a formula can be derived for the
atomic number of the stable isobar Z_{s}.
Z_{s} = A (1 + 0.0071 A^{-1/3}) (1.983 + 0.016
A^{2/3})^{-1}
For example, for mass number 123, it can be shown that the atomic
number for the stable isobar is 51.8. This is in agreement with the observed
result.
For a lighter nuclide with A = 57, the above
formula gives Z_{s} = 32. However, the stable isobar
with mass 57 is iron, Z = 26. The error is very large.
The merit of the semi-empirical formula
Theorization is an important step in science. A theory is a catalyst for
progress. The semi-empirical equation for binding energy is based on
the liquid drop model for nuclear structures, and the coefficients are
derived by using a large number of data. Thus, the equation is
the result of semi-empirical approach.