Reminder The LS coupling hierarchy

Reminder The LS coupling hierarchy

Reminder Term Symbols

Reminder Hund’s rules

Reminder Spin-orbit coupling

Reminder LS coupling hierarchy

jj coupling hierarchy

jj coupling hierarchy: the term symbols

L and S are no longer good quantum numbers

Only j1, j2, …, J are good quantum numbers

… is the term symbol in jj coupling.

Transition from LS to jj coupling: a «correlation diagram»

Transition from LS to jj coupling: a «correlation diagram»

Database of atomic levels:https://physics.nist.gov/PhysRefData/ASD/levels_form.html

Hyperfine coupling

Magnetic moment in classical physics

re-

v

m

Using the correspondence principle

Hyperfine coupling

Hyperfine coupling

Hyperfine coupling

Quantum numbers:

Hamiltonian: H α α^

Light-matter interaction operator within dipole approximation is:

For light linearly polarized along the Z axis:

Generally true:

Within validity of LS-coupling:

For one-electron transitions:

Eigenvalues:

Selection rules:

Electric-dipole-moment operator𝑀 transforms as coordinates (x,y,z) parity -1

Spectra of hydrogen and one-electron atoms

Spectra of hydrogen and one-electron atoms

Fine and hyperfine structure of hydrogen: the n=1 and n=2 manifolds

1s L=l=0, S=s=1/2

2s L=l=0, S=s=1/2

2p L=l=1, S=s=1/2

2p L=l=1, S=s=1/2

Spectra of alkali-metal atoms

Fine and hyperfine structure in the spectra of alkali-metal atoms

Spectra of the rare-gas atoms

Configuration:

l1=1, l2=0, s1=s2=1/2

l1=1, l2=2, s1=s2=1/2

LS coupling

L=1; S=0,1

L=1,2,3; S=0,1

jj coupling

j1=1/2,3/2; j2=1/2

(1/2,1/2)1,(3/2,1/2)1

j1=1/2,3/2; j2=3/2,5/2

(1/2,3/2)1,(3/2,3/2)1,(3/2,5/2)1

NEW: jk coupling

𝑗1 + 𝑙2 = 𝑘

𝑘 + 𝑠2 = Ԧ𝐽

Notation: (j1,l2,k)J or (2Pj1)nl2[k]J

j1=1/2,3/2; k=1/2,3/2

(2P1/2)ns[1/2]1,(2P3/2)ns[3/2]1

j1=1/2,3/2; k=1/2, 3/2, 5/2, 7/2

(2P1/2)nd[3/2]1,(2P3/2)nd[1/2]1 ,(2P3/2)nd[3/2]1

Spectra of the rare-gas atoms

Configuration:

l1=1, l2=0, s1=s2=1/2

l1=1, l2=2, s1=s2=1/2

NEW: jk coupling

j1=1/2,3/2; k=1/2,3/2

(2P1/2)ns[1/2]1,(2P3/2)ns[3/2]1

j1=1/2,3/2; k=1/2, 3/2, 5/2, 7/2

(2P1/2)nd[3/2]1,(2P3/2)nd[1/2]1 ,(2P3/2)nd[3/2]1

Spectra of the rare-gas atoms

1S0

Spectra of the rare-gas atoms

1S0

«autoionization»

«diffuse»

«sharp»