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Homework Help: Electric Dipole Transition

  1. Feb 25, 2010 #1
    have another problem with one of my exercises
    1. The problem statement, all variables and given/known data
    Make a crude estimate for the mean life of an electric dipole transition

    in a atom [tex]E_\gamma = 10 eV[/tex]
    in a nucleus [tex]E_\gamma = 1 MeV[/tex]

    2. Relevant equations
    [tex]W_{\alpha \beta} &=& \frac{4}{3} \frac{e^2}{\hbar^4 c^3} E_\gamma^3 |<\beta|\vec{x}|\alpha>|^2 \
    &=& \frac{4}{3} \frac{\alpha}{\hbar^3 c^2} E_\gamma^3 |<\beta|\vec{x}|\alpha>|^2 [/tex]
    with the first \alpha beeing the fine structure constant [tex]\alpha = \frac{e^2}{\hbar c}=\frac{1}{137} [/tex]

    3. The attempt at a solution
    I am not quite sure how to estimate the last factor in the equation. Since we just have to do a crude estimate i dont think we have to calculate it with real wavefunctions(dont know if there are even wavefunctions for nuclei)
    So my first thought was since [tex]|<\beta|\vec{x}|\alpha>|^2[/tex] has the dimension of a length^2 I inserted the typical lengthscales of an atom, the Bohr radius, and for the nucleus 1fm.
    For the atom I get W= 1.1 10^9 1/s and for the nucleus 3.82 *10^14 1/s.
    The lifetime is just the inverse of these. But I think the lifetime is then too small, I have something like 10^(-8) in my mind for the atom.
    Anyone has a idea how to estimate it in a better way?

  2. jcsd
  3. Feb 25, 2010 #2


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    Crude estimates of this type are usually handled with the Uncertainty principle.
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