- #1
KeepWondering
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In the straight-forward derivation of the Kramer-Heisenberg formula describing the photon-atom scattering cross section (to second order perturbation theory, see e.g. the path leading to https://quantummechanics.ucsd.edu/ph130a/130_notes/node470.html), the finite lifetimes of the intermediate states and their natural linewidth, respectively, do not (explicitly?!) show up. As their neglection would cause an infinite coupling for resonant scattering, the linewidths are included subsequently and manually (after the rigorous derivation) without justification.
One possible justification could be, that the linewidth show up when the derivation includes higher order perturbation theory. But I doubt this.
Another approach could be linked to the question: Which states are actually included in the generic "sum over all intermediate states"? Does it include just all "classical" atomic eigenstates? Or rather any discrete energy levels/states from the ground state to the ionisation energy threshold possibly discretised by ΔE = h/(2π τplanck)?
This would perfectly solve the problem because the linewidth is already included in the sum since the very beginning of the rigorous derivation. In consequence, we/I/the notation however would have to change from the comfortable concept that there are some "special" atomic energy states due to the quantum numbers to the concept of purely dynamic intra-atomic behaviour where all energy steps n*h/(2π τplanck) are basically allowed and in principle identical in their physical nature except of their different lifetimes.
Can someone provide a justification?
Many thanks in advance!
One possible justification could be, that the linewidth show up when the derivation includes higher order perturbation theory. But I doubt this.
Another approach could be linked to the question: Which states are actually included in the generic "sum over all intermediate states"? Does it include just all "classical" atomic eigenstates? Or rather any discrete energy levels/states from the ground state to the ionisation energy threshold possibly discretised by ΔE = h/(2π τplanck)?
This would perfectly solve the problem because the linewidth is already included in the sum since the very beginning of the rigorous derivation. In consequence, we/I/the notation however would have to change from the comfortable concept that there are some "special" atomic energy states due to the quantum numbers to the concept of purely dynamic intra-atomic behaviour where all energy steps n*h/(2π τplanck) are basically allowed and in principle identical in their physical nature except of their different lifetimes.
Can someone provide a justification?
Many thanks in advance!