reminder the ls coupling hierarchy...jj coupling hierarchy: the term symbols l and s are no longer...
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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»