The masses of a set of isobars is given by:
Let us cast this in the form of the deviation from the mass of the most
stable of this set. Putting
and using
,
where
is the mass of the most stable isobar (for the given A).
Thus for the odd-A nuclei (i.e. even-odd),
and for even-A nuclei
Thus the masses of odd-A nuclei are distributed along a parabola,
while those for even-A nuclei alternate between two parabolas
separated by
. Since adjacent isobars are linked by beta
decays, this has important consequences for the sequence of decays to
the most stable isobar. In particular, there are likely to be two stable
isobars for even A, having adjacent even Z and both being unable to
decay to the odd Z isobar between them. For odd-A isobars there is
only one stable isobar. (So, how many stable nuclei are there for
?).