Qualitative explanation of radiative transitions and selection rules.

  1. Hi,
    I'm looking get a deeper conceptual grip on A&M spectroscopy, particularly what actually goes on between atoms/molecules and photons during an emission/absorption event. In general I just want to understand the "why's and how's" of the selection rules for dipole/quadrupole transitions, but more immediately I'm looking to understand how polarized light is created/absorbed by an atom (which depends on what Δm_l turns out to be during the transition).

    I've done the derivations on the subject in Sakurai's book (modern QM, section on dipole transitions) but I feel none the wiser, haven't found anything satisfying in my go-to QM text (Cohen-Tannoudji).

    There's a qualitative explanation of radiative transitions and selection rules in Fowles' "Modern Optics", pg. 244 which I've never found in any standard QM book or in my spectroscopy course/book. Can be found here:

    http://books.google.es/books?id=SL1n9TuJ5YMC&lpg=PA203&pg=PA244#v=onepage&q&f=false

    What is meant precisely by the "coherent state between 1s+2p(m=±1)" (caption on fig. 8)? Does this refer to some intermediate state between before and after absorbing/emitting the photon that only lasts for a period of 2π/ω ?

    What exactly is happening to the atom's state vector here, how is it evolving from a state (say) |n,l=0,ml=0> → |n+1,l=1,ml=1> when it absorbs a photon?

    What is the physical explanation for the dipole selection rule in this transition (ml must change by an integer value), ie: why is the atom's orbital AM forced to change direction?

    Where can I expand on this and and/or find a justification of the selection rules? Any particularly good text/chapter from a text worth consulting?
     
    Last edited: Nov 23, 2013
  2. jcsd
  3. atyy

    atyy 11,035
    Science Advisor

  4. Start with H atoms, and the allowed electronic transition from the doublet S state (where the electron is in the 1s orbital) to the doublet P state (where the electron is in a 2p orbital). For electric dipole transitions, an electric dipole in the atom or molecule is set to oscillating by the photon's oscillating electric field. In this case, the only electric dipole available is that between the electron and the nucleus. The state of the electron must be described by a linear combination of two orbitals (in the simplest description). The initial state is spherically symmetrical, so the final state must include a displacement of the electron from that symmetry. The 2p orbital does that. On the other hand, the 2s orbital is also spherically symmetrical, so it doesn't; and so the doublet 1S to doublet 2S transition is electric-dipole forbidden.

    You can extrapolate that idea to explain, for instance, IR absorption in a molecule. The electric dipole in the molecule must be set oscillating by the oscillating electric field. Keep in mind that classically, an oscillating force transfers energy most efficiently when it's frequency matches the natural frequency of the oscillator; that's why the IR spectrum shows absorption peaks when the photon frequency matches the molecular vibrational frequency.

    All the other cases (including magnetic dipole, electric quadrupole, etc.) can be viewed this (semi-classical) way. I suggest you take a look at Walter Kauzmann's Quantum Chemistry. It's an old book from the 50s, but is very well-written and uses this kind of semiclassical reasoning extensively. E.g., he has a great explanation for circular dichroism based on considering the current flow in a helical spring--there's left-handed and right-handed, etc.

    Maybe 15 years ago the Journal of Chemical Education published some animations of the H atom transitions that helped me to visualize this. Look there.
     
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