Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Cross Section Question

  1. Jul 29, 2009 #1
    I know the formulas for the length and velocity forms of the photodetachment cross section for an electron with energy [tex]\hbar\omega[/tex] are, respectively,

    [tex]\sigma_{L}(\omega)=\frac{4\pi^{2}\alpha a_{0}^{2}\omega}{3}\sum_{f}|\langle\Psi_{f}|\sum_{j=1}^{n}z_{j}|\Psi_{i}\rangle|^{2}[/tex]


    [tex]\sigma_{V}(\omega)=\frac{4\pi^{2}\alpha a_{0}^{2}\omega}{3}\sum_{f}|\langle\Psi_{f}|\sum_{j=1}^{n}\frac{\nabla_{j}^{z}}{i\omega}|\Psi_{i}\rangle|^{2}.[/tex]

    Could someone please explain what these actually mean and how they are derived, or even better, where I can find a good reference on them? I asked my research professor about them and he was no help (these are where I got them from), and I can't find anything about them on the internet.
  2. jcsd
  3. Aug 21, 2009 #2


    User Avatar
    Homework Helper

    try Sakurai's quantum mechanics book. Look up Fermi's Golden Rule.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook