= fine structure constant
expansion factor is = fine structure constant
Lengths:
= classical electron radius
= rydberg energy
so the relativistic corrections are small.
Energy levels:
for single electron atoms.
with 
a typical k is 
where a = seperation
of atoms in molecule. Then 
so a typical energy would be 
.
.with 
so 
so a typical energy would be
Dipole radiation:
For a free charge: 
. Characteristic dipole is
. For electronic and vibrational, this is a transitional moment,
while for rotational this is a permanent moment.
. This is 
for the lyman alpha. For a rotational
system it would be: 
because of the scalings of energies. 
. This
means ions may have to wait a long time to become unionized, since
radiative capture chances are so low.