The atom in magnetic field Orbital and spin magnetic moment of the - - PDF document

The atom in magnetic field

Orbital and spin magnetic moment

• f 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 B2 term can be neglected if the atom has magnetic moment (is important only for diamagnetic atoms) The perturbation potential The representation in which Lz 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 H0
• The energy of the interaction with the magnetic field
• Taking into account the spin-orbit interaction

are not eigenstates of L2 and S2, only of Lz and Sz, and in the interaction with the magnetic field

• nly 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