Zeeman effect HFS and isotope shift
Anomalous Zeeman Effect
• More than three closely spaced optical lines were observed.
• The interaction that splits the energy levels in an external magnetic field
is caused by
interaction.
• The magnetic moment depends on
Orbital contribution
and
Spin magnetic moment
• The 2J + 1 degeneracy for a given total angular momentum state J is
removed by the effect of the
.
• If the
is small compared to internal magnetic field, then and
precess about while precesses slowly about
.
•
<= 0.1T for Zeeman splitting
• The normal Zeeman affect occurs for S=0
Nuclear shell model
HFS and isotope shift
F
5/2
1
B
4
(5/2)A
wj
IS

3/2
3
J
2
I 1
B
(3/2)A
1/2
HFS levels:
for Q=0

full lines
B>0
broken lines B < 0
3
C (C  1)  I ( I  1) J ( J  1)
C
wF  wJ  A
B 4
2
2 I (2 I  1) J (2 J  1)
with
A
C  F ( F  1)  I ( I  1)  J ( J  1)
F  I  J , I  J  1,...., I  J
 I H ( 0)
IJ
B  eQ  JJ (0)
5
B
4
n (r)
Field isotope shift:
A
Á
r0
E F    e ( r ) ( r )4r 2 dr
r
0
e 
charge density
of s electrons at
the site of the nucleus
r0
r0
 (r )
 (r )
 FAÁ   AA   AÁ
AÁ



C

AA
2
2k 
k
 F1  r   AÁ  r   E1AÁ  E1AÁ  r 2


k 2 C1
This amounts to a few percent