Zeeman Effect: Counting Frequencies and Explaining Zero Frequency

[KFC]

Suppose for a system with two levels with corresponding rotational quantum number J=2 and J=1, each of these have sublevels corresponding to J=2: m_J=-2, -1, 0, 1, 2 and J=1: m_J=-1, 0, 1, tune the external field such that we have transitions corresponds to \Delta m_J=-1, 0, 1. So how many different frequencies will be observed? And for the transition \Delta m_J=0, does it mean the corresponding observed frequency is ZERO? How come?

 

[Rajini]

hi,
for your 1st question: 9.
2nd question: i guess freq. won't be zero..

 

[KFC]

Thanks. For the second question, I think I make a mistake, I forget that the Zeeman term is just the correction of the energy, so the frequency will not be zero.

But for the first question, someone said though there are 9 different transitions but only 5 frequencies are distinct, why?

 

[Rajini]

I don't know sorry..But it may be something to do with relaxations between sub-states..
May i know where you got to know that 5 freq. are distinct..some book?

 

[ytuab]

Suppose for a system with two levels with corresponding rotational quantum number J=2 and J=1, each of these have sublevels corresponding to J=2: m_J=-2, -1, 0, 1, 2 and J=1: m_J=-1, 0, 1, tune the external field such that we have transitions corresponds to \Delta m_J=-1, 0, 1. So how many different frequencies will be observed?

The Zeeman effect has about three patterns as follows. (the external magnetic field is the z direction.)

1 J_{Z} is an integer, which means the electron number is even. The normal Zeeman effect is seen (in the case of the sum of the spin is zero.(equal triplet pattern due to the selection rule (\Delta J = +1,0,-1).))

2 J_{Z} is not an integer(1/2, 3/2, 5/2...). When the magnetic field is strong, the Paschen-Back effect is seen. (S_{Z} is 1/2, so the z component of the spin magnetic moment is the Bohr magneton(due to 2 x 1/2 =1)).

3 When the magnetic field is weak, the anomalous Zeeman effect is seen. Strange to say, in this case S_{Z} is not exactly 1/2 and it's changing continuously. Because this includes three rotations as follows,
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Rotation (spin + orbital)

Precession(1) ---- The combined magnetic moment \vec{\mu}=2\vec{S}+\vec{L} precesses about \vec{J}=\vec{S}+\vec{L}(not \vec{J_{Z}}).
(But I think this precession is very strange. Why does this precession occur? Because the \vec{J} is an angular mometum, not the magnetic moment. So this direction has no relation to the direction of the force such as the magnetic field(\vec{Z} or the magnetic moment\vec{\mu}, 2\vec{S}, or \vec{L}{.)

Precession(2) ----- The \vec{J} component of the \vec{\mu} precesses about Z axis.
See this Google book (in page 238).
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I think your case is 1. So it's the normal Zeeman triplet=3 patten. OK?