Undergrad Decoupling of angular momentum

[kelly0303]

Hello! I am reading some papers and I often noticed that it is mentioned that a strong magnetic field is able to decouple certain angular momenta from each other. For example in this paper: https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.100.023003 they present a Hamiltonian (second column on the first page) that contains terms of the form $\gamma N\cdot S + b I\cdot S$, where S is the spin of the electron, I is the nuclear spin and N is the rotational quantum number of the molecule rotation. Then, after a strong enough magnetic field is applied, B is able to decouple S from I and N. I am not sure I understand what does this mean. If we add a magnetic field, shouldn't we just add another term to the hamiltonian so the new hamiltonian would be (ignoring the terms I ignored in the first part, too), $\gamma N\cdot S + b I\cdot S - g\mu_B S\cdot B$ i.e. the spin, S, is obviously feeling the magnetic field, but it also feels the N and I. Why would a magnetic field make the 2 terms containing I and N disappear? Can someone explain to me what this decoupling means? Thank you!

 

[DrClaude]

You have to look at it from the perspective of perturbation theory. Adding the magnetic field tot he Hamiltonian will of course not remove one of the terms already present, but the hierarchy of the terms will dictate how certain quantum numbers are or are not useful to study the energy levels.

A good example of this is the Paschen-Back effect:
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/paschen.html

 

[kelly0303]

You have to look at it from the perspective of perturbation theory. Adding the magnetic field tot he Hamiltonian will of course not remove one of the terms already present, but the hierarchy of the terms will dictate how certain quantum numbers are or are not useful to study the energy levels.

A good example of this is the Paschen-Back effect:
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/paschen.html

Thanks a lot for this! So by these "coupling" and "decoupling", they just mean what terms in the Hamiltoninan are dominant, and hence, which quantum numbers are (almost) good to be used in perturbation theory?

 

[DrClaude]

Thanks a lot for this! So by these "coupling" and "decoupling", they just mean what terms in the Hamiltoninan are dominant, and hence, which quantum numbers are (almost) good to be used in perturbation theory?

Yes. Think back to LS coupling vs jj-coupling in atoms, where it is the relative strength of the spin-orbit interaction compared to the residual electrostatic interaction that decides whether it is useful to describe the states using term symbols, $^{2S+1}L_J$, or whether $L$ and $S$ have no relevance due to $l$ and $s$ coupling into $j$ for each electron first.

 

[vanhees71]

This is another example of the fact that most of the weirdness of QT is related to the weird slang people developed talking about it (particularly Bohr and Heisenberg were the masters of destaster)