• The total angular momentum • The energy depends on j!• Second-order approximation
Stationary perturbational method
The perturbational treatment of the relativistic effect
If the Dirac equation is expanded in terms of v2/c2, one obtains 3 correction terms:
• the relativistic correction of the kinetic energy
• the Darwin-term (only for l=0)
• the spin-orbit interaction term
Perturbation theory for a degenerate levelIs desirable that the perturbation LS to be diagonalThis is valid in the representation |lsjmj>,because L2, S2, J2 and Jz commute with LS.
We write the scalar product as
The diagonal matrix element is
It can be calculated analytically
Finally
Adding these contributions, the terms depending on l cancel out.
The difference between the two splitted levels (the spin-orbit splitting)
Lamb shift – quantum field theory
The Lamb shift experiment
Slight changes in the electromagnetic force
Hyperfine splitting• The magnetic momentum of the nucleus
• The interaction with the magnetic moment of the electron (for l=0)