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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?

Bye

Fluffy

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# Homework Help: Electric Dipole Transition

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