Download The atom in magnetic field

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 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
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