In my atomic lecture notes we prove (at least for electric dipole transitions), that only one electron can 'jump' at once.

The proof is as follows. The matrix element (assuming distinguishable electrons for now with understand that the real state would involve a Slater determinant) for a multi electron transition is e.g. $$\propto \langle \psi_1(1s) \psi_1(2p)|\vec{r_2} + \vec{r_2}|\psi_1(3p)\psi_2(3d)\rangle$$ $$=\langle \psi_1(1s)|\vec{r_1}|\psi_1(3p)\rangle \times\langle\psi_2(3p)|\psi_2(3d)\rangle $$ $$+ \langle \psi_2(2p)|\vec{r_2}|\psi_2(3d)\rangle \times\langle\psi_1(1s)|\psi_1(3p)\rangle$$ $$=0+0=0$$

My question is whether this property of 'only single electron jumps allowed' is unique to just electric dipole transitions, or just for treating atoms under central field approximation etc, or is this a general property of transitions. If multiple electron transitions are possible, in what cases are they possible?

  • $\begingroup$ Just as a note (which doesn't aswer the math in your question): In any multielectron system, if one electron changes its orbital, the potential felt by the other electrons changes. Hence they also need to adapt the shape of their orbitals. This is why one doesn't talk about single electrons changing their state, but the whole atom does so. $\endgroup$ – A. P. Feb 11 at 9:17

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