The atom in magnetic field
Orbital and spin magnetic moment of the electron The Bohr-magneton (1/ 2 in atomic units) •
The Hamiltonian for the interaction with the magnetic field B has Oz direction •
The normal Zeeman effect (S= 0) A – the vector potential B= rot A • For homogeneous magnetic field • where we have used
The B 2 term can be neglected if the atom has magnetic moment (is important only for diamagnetic atoms) The perturbation potential The representation in which L z is diagonal The energy correction
The normal Zeeman effect (S= 0) The spectral lines
The atom in strong magnetic field The interaction with the magnetic field is stronger than • the spin-orbit interaction The eigenstates of H 0 • The energy of the interaction with the magnetic field • Taking into account the spin-orbit interaction •
are not eigenstates of L 2 and S 2 , only of L z and S z , and in the interaction with the magnetic field only the z of the component is conserved. This splitting of the energy levels because of the spin-orbit interaction in a strong magnetic field is called the Paschen-Back effect. The total energy correction:
Atoms in weak magnetic field – the anomal Zeeman effect The unperturbed energy level is characterized by kLSJ, the spin-orbit coupling is not broken. The interaction with the magnetic field in this case is the same as before
The energy correction may be written as • we use the relation • Taking only the 0z component
We obtain for the matrix element and for the energy correction the Lande factor 2j+ 1 magnetic sublevels
Zeeman effect for sodium
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