expansion factor is = fine structure constant

Lengths:

• = classical electron radius
• 
• 
• = rydberg energy

so the relativistic corrections are small.

Energy levels:

• 
• for single electron atoms.
• fine structure: of order
• hyperfine structure of order
• vibrational energy levels: with a typical k is where a = seperation of atoms in molecule. Then so a typical energy would be .
• rotational energy levels: .with so so a typical energy would be

Dipole radiation:

• power radiated is: For a free charge: . Characteristic dipole is . For electronic and vibrational, this is a transitional moment, while for rotational this is a permanent moment.
• spontaneous emission: . 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.