Atomic Physics

Configurations in Ne I
pd-configuration LS-coupling
Configuration
Term
Central field
Repulsion
Numerical example for 2p3d in O V, energies in cm-1
E(2p3d) = 701810 Kinetic and central part of electrostatic
∆E (P - D) = 8980
Direct part of electrostatic repulsion
∆E (1F - 3F) = 15074 Exchange part of electrostatic repulsion
pd-configuration LSJ-coupling
Configuration
Term
Level
Central field
Repulsion
Spin-orbit
Numerical example for 2p3d in O V, energies in cm-1
E(2p3d) = 701810 Kinetic and central part of electrostatic
∆E (P - D) = 8980
Direct part of electrostatic repulsion
∆E (1F - 3F) = 15074 Exchange part of electrostatic repulsion
∆E (3F4- 3F3) = 235 Spin-orbit magnetic energy
Degeneracy – statistical weight, g, in a
pd-configuration.
g ( E ) 60,
g (3 D) (2 L 1) (2 S 1) 15
g (3 D3 ) 2 J 1 7
Elektronens magnetisk moment pga banrörelsen
 
e
2m
Stern-Gerlach experiment. Electron spin.
A beam of neutral silver atoms pass through an
inhomogeneous magnetic field directed in the z-direction.
Silver has a ground configuration with filled orbitals and an
unpaired 5s outer electron, hence L = 0 and μL = 0
Still the Ag-beam split into 2, which can be explanined by
assuming that the electron has an intrinsic angular
momentum – spin – and with that an associated magnetic
moment μS.
s  gs
e
2m
s,
gs  2
Magnetiska dipolmoment
e
L
µL = −
2m
e
2
− gs ⋅
⋅ S , gs =
µS =
2m
e
−
⋅ ( L + 2S )
µ tot =
2m
Vi ska studera 3 magnetiska effekter i en atom. Energin
ges alltid av E =− µ ⋅ B så vårt jobb är att bestämma hur
momentet respektive magnetfältet kan beräknas
• Spinn-ban växelverkan: H SO =
− µ S ⋅ BL - klart
• Hyperfinväxelverkan – nästa LP
• Atomer i ett yttre magnetfält:
• Zeemaneffekt
• Paschen-Back effekt
Enheter
Här: L  , µ = −
e
L
2m
Foot: L  1, µ = − µ B L , µ B (Bohr magnetonen) =
e
2m
Zeeman effect in the vector model
J

   J  e J     e
Weak field =>
 L and S precess much faster around J than J
around B
 The net effect of   is zero
pd-configuration LSJ-coupling and a
magnetic field
Configuration
Term
Level
Sublevel
Central field
Repulsion
Spin-orbit
Mag. Field
Numerical example for 2p3d in O V, energies in cm-1
E(2p3d) = 701810
∆E (P - D) = 8980
∆E (1F - 3F) = 15074
∆E (3F4- 3F3) = 235
∆Emag (2 - 1) =
0,7
Kinetic and central part of electrostatic
Direct part of electrostatic repulsion
Exchange part of electrostatic repulsion
Spin-orbit magnetic energy
Magnetic energy separation in a 1T field
Urvalsregler för E1 (elektisk dipol) strålning
J = 0, 1 ej 0 → 0
Endast en elektron får ändra orbital, n → n’’
= 1
MJ = 0, 1 ej 0 → 0 om J = 0
I perfekt LS-koppling
S=0
L = 0, 1 ej 0 → 0
Zeeman effect and the polarization of light
Viewed in absorption: M J  1    , M J  0  
Polarization of Zeeman light
An arbitrary motion in 3-dim can be described in Cartesian
coordinates or by combining a linear and 2 opposite circular
motions
Magnetic effects on the spectrum from a white
dwarf. Magnetic field about 6000 T!!
(Paschen-Back effect)
Balmer-beta
Balmer - alpha
Zeeman vs. Paschen-Back in a 3P
Zeeman
E  E (3 P ) 
1
 LS  [ J ( J  1)  L( L  1)  S ( S  1)] 
2
B  B  g J  M J
B B 
1
 LS
10
3
P
Paschen-Back
E  E (3 P ) 
 B  B  ( M L  2M S ) 
 LS  M L  M S
 B B  10   LS
3
P