Anamolous zeeman effect

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1. Russell Saunders coupling and J-J coupling
& Anomalous Zeeman Effect and Paschen
Back effect
PRESENTS BY
PRADEEPKUMAR YADAV
RAMNIRANJAN JHUNJHUNWALA
COLLEGE
MSC – II ( PHYSICAL CHEMISTRY )
SEM – III (2013 – 14)

2. Zeeman effect
A splitting of the energy terms of atoms in a magnetic field can
be observed as a splitting of the frequencies of transitions in the
optical spectra (or as a shift). A splitting of this type of spectral
lines in a magnetic field was observed for the first time in 1896
by Zeeman.
The effect is small. Spectral apparatus of very high resolution is
required. These are either diffraction grating spectrometers with
long focal lengths and a large number of lines per cm in the
grating, or else interference spectrometers, mainly Fabry-Perot
interferometers.
With a Fabry-Perot interferometers or with a grating
spectrometer of sufficient resolution, the splitting in magnetic
fields may be quantitatively measured.

3. Fabry-Perot Interferometer
This interferometer makes use of multiple reflections
between two closely spaced partially silvered surfaces.
Part of the light is transmitted each time the light reaches
the second surface, resulting in multiple offset beams
which can interfere with each other. The large number of
interfering rays produces an interferometer with
extremely high resolution (10
6
), somewhat like the
multiple slits of a diffraction grating increase its
resolution.

4. Without magnetic field
With magnetic field
The D lines of sodium. The D
1
line splits into four components, the D
2

line into six in a magnetic field. The wavelengths of the D
1
and D
2

lines are 5896 and 5889 nm; the quantum energy increases to the right
in the diagram.
D
1
D
2
The anomalous Zeeman effect

5. The Zeeman effect results from the splitting of energy states
with the interaction of the resultant angular momentum and
external magnetic fields.
If the resultant angular momentum is composed of both spin
and orbital angular momentum, one speaks of the anomalous
Zeeman effect.
The normal Zeeman effect describes states in which no spin
magnetism occurs, therefore with pure orbital angular
momentum. In these states, at least two electrons contribute in
such a way that their spins are coupled to zero. Therefore, the
normal Zeeman effect is found only for states involving several
(at least two) electrons.

6. In general case, the atomic magnetism is due to the
superposition of spin and orbital magnetism, which results the
anomalous Zeeman effect.
In cases of the anomalous Zeeman effect, the two terms
involved in the optical transition have different g factors,
because the relative contributions of spin and orbital
magnetism to the two states are different. The g factors are
determined by the total angular momentum j and are therefore
called g
j
factors. The splitting of the terms in the ground and
excited states is therefore different, in contrast to the situation
in the normal Zeeman effect.

7. The magnetic moments in the direction of the
field are
Bjjzjj gmmm -=
,)(
The magnetic energy is
0,
1
BgE
Bjmm
jj
m=D
-
0,
)( BV
zjjm
j
m-=
The number of splitting components in the field is given by m
j
and is
again 2j+1. The distance between the components with different
values of m
j
– is-called Zeeman components – is no longer the same
for all terms, but depends on the quantum numbers l, s, and j:

8. The paschen-Back effect
The spin-orbit coupling is stronger than the coupling of either the
spin or the orbital moment alone to the external magnetic field.
When the magnetic field B
0
is strong enough so that the above
condition is no longer fulfilled, the splitting picture is simplified.
The magnetic field dissolves the fine structure coupling. L and s are,
to a first approximation, uncoupled, and process independently
around B
0
. The quantum number for the total angular momentum j,
thus loses its meaning. This limiting case is called the Paschen-Back
effect.

9. The Pachen-Back effect
In a strong magnetic field B
0
, the
spin S and orbital L angular
momenta align independently with
the field B
0
. A total angular
momentum J is not defined.
The components of the orbital (µ
l
)
z
and
spin (µ
s
)
z
moments in the field
direction are now individually
quantised. The corresponding
magnetic energy is
0, )2( BmmV
Bslmm
ls
m+=
The splitting of the spectral lines:
0
)2( BmmE
Bsl
mD+D=D

10. LS coupling (Russell-Saunders coupling)
If the spin-orbit interactions (s
i
· l
i
) between the spin and orbital angular
momenta of the individual electrons i are smaller than the mutual
interactions of the orbital or spin angular momenta of different electrons
coupling (l
i
· l
j
) or (s
i
· s
j
), the orbital angular momenta l
i
combine to a total
orbital angular momentum L, and the spins combine to a total spin S. L
couples with S to form the total angular momentum J.
LSJ
sS
lL
i
i
i
i



+=
=
=
å
å
,
,

11. LS coupling gives a good agreement with the observed
spectral details for many light atoms. For heavier atoms,
another coupling scheme called j-j coupling provides better
agreement with experiment.
The vector model:

12. For example for a two-electron system like the He atom
212121
21
,,1,
)1(,
llllllL
LLLllL
--++=
+=+=



The orbital angular momentum L of the atom:
The quantum number L determines the term characteristics:
L = 0, 1, 2, … indicates S, P, D, … terms.
It should be noted here that a term with L = 1 is called a P
term but this does not necessarily mean that in this
configuration one of the electrons is individually in a p state.

13. For the total spin angular momentum S:


)1(
21
+=+= SSSwithssS
The spin quantum number:
S = ½ + ½ = 1 or S = ½ - ½ = 0
The interaction between S and the magnetic field B
L
, which arises
from the total orbital angular momentum L, results in a coupling
of the two angular momenta L and S to the total angular
momentum J:


)1(, +=+= JJJSLJ
The quantum number J:
For S = 0, J = L; singlet;
For S = 1, J = L +1, L, L – 1triplet

14. jj coupling
jj coupling is the case for coupling of electron spin and orbital
angular momenta is larger compared to the interactions (l
i
· l
j
)
and (s
i
· s
j
) between different electrons. It occurs mostly in
heavy atoms, because the spin-orbit coupling for each
individual electron increases rapidly with the nuclear charge Z.





)1(
;
;
222
111
+==
+=
+=
å JJJwithjJ
slj
slj
i

15. In jj coupling, a resultant orbital angular momentum L is not
defined. There are therefore no term symbols S, P, D, etc. one
has to use the term notation (j
1
, j
2
) etc..
The number of possible states and the J values are the same as
in LS coupling.
A selection rule for optical transitions:
DJ = 0, ±1, and a transition from J = 0 to J = 0 is forbidden.
Purely jj coupling is only found in very heavy atoms. In most
cases there are intermediate forms of coupling (intermediary
coupling), which the intercombination between terms of
different multiplicity is not so strictly forbidden.

16. REFERENCE
Atkins P.W, Physical Chemistry, Oxford
University Press, 6th edition, 1998
James E. House, Fundamentals of Quantum
Chemistry, Second Ed.,
Academic Press, 2005
R. K. Prasad, Quantum Chemistry, 3rd Ed.,
New Age International
Publishers, 2006