# Is this transition allowed or forbidden?

1. Dec 8, 2016

### Poirot

1. The problem statement, all variables and given/known data
Under the multi-electron electric dipole (E1) selections rules, state whether this transition is allowed or forbidden and state which selection rule(s) has been violated.
for He: 1s1p 1P1-> 1s2 1S1
2. Relevant equations
For E1:
\begin{eqnarray*} Parity \ changes: (-1)^l\\
\Delta L = 0, \pm 1 (0\rightarrow{}0 \ not \ allowed)\\
\Delta J = 0, \pm 1 (0\rightarrow{}0 \ not \ allowed)\\
\Delta S = 0\end{eqnarray*}

3. The attempt at a solution
The initial state has: L=1, 2S+1=1 so S=0, J=1
Final state has: L=0, 2S+1=1 so S=0, J=0

so in theory this is allowed because ΔL=-1, ΔS=0 and ΔJ=-1, but I'm not sure how to implement the parity condition? Is it that because the electron is initially in 1p, l=1 and then ends in 1s^2 so l=0 so this transition is odd and parity is fine?
I have a feeling this is physically impossible because I don't think 1p exists? I'm quite lost here so any help would be great!

2. Dec 8, 2016

### eys_physics

The parity of the state is $(-1)^L$, i.e. negative for the initial state and positive for the final state.
You can also this in terms of the individual electron configurations
For the initial state: $(-1)^0\times (-1)^1=-1$, in a similar way you should be able to get that the final state has positive parity.
I don't see why the 1p state cannot exist? What is your arguments for this?

3. Dec 8, 2016

### TSny

1p would imply a p-state for n = 1, which doesn't exist. I think there must have been a misprint in the original statement of the problem. Maybe the configuration for the initial state was meant to be 1s2p.

4. Dec 9, 2016

### Poirot

Do you do (-1)^l for each electron in the shell? or just the l for that shell, so for example if you had:
1s2 2s2 2p 3s
would the parity calculation be: (-1)0(-1)0(-1)1(-1)0 = -1

or is it per electron?

And as for the 1s1p, I think it must be a typo.

5. Dec 9, 2016

### eys_physics

Yes, probably it should be 2p. First I was not aware of the restrictions on the n quantum since I am not an expert in atomic physics.

Yes, you are correct regarding the parity. Total parity of a state is the product of the parities of the individual states.
This is easy to understand from the definition of parity. If the parity is -1 you have $$\phi(-\mathbf{r})=-\phi(-\mathbf{r})$$ and if parity is 1, $$\phi(\mathbf{r})=\phi(-\mathbf{r})$$ for the wave function.

6. Dec 9, 2016