Parity of a system composed by 2 particles

[bznm]

I have read that for a system of 2 particles, the total parity is given by:

P=P_1 P_2 (-1)^L where

- P_1, P_2= insisec parity of particle 1, 2

- L= relative angular moment

what's the meaning of "relative angular moment"? Do I have to add the l numbers of the two particles? And what if I have 3 particles?

Many thanks

 

[Einj]

L is the "relative" angular momentum, which means that is the momentum of the system of the two particles "orbiting around each other" if considered as a whole.

If you have three particles you need to first study two of them and obtain the corresponding system and then compose this last system with the third particle.

 

[bznm]

L is the "relative" angular momentum, which means that is the momentum of the system of the two particles "orbiting around each other" if considered as a whole.

If you have three particles you need to first study two of them and obtain the corresponding system and then compose this last system with the third particle.

Thanks for your answer. But I have no ideas about what I have to do in practice... For example, let's consider a pion and a deuterium. I know that the pion is captured in s-wave by the deuterium and it was told me that (-1)^L =1, but I don't understand why. Could you help me?

 

[Einj]

The nomenclature is S-wave (L=0), P-wave (L=1), D-wave (L=2), etc.

 

[bznm]

I imagined it... but I haven't understood what is a "S-wave". The fist - and last - time that I have heard it, the prof said "The deuterium captures the pion in S-wave". Could you explain me briefly in which way "S-wave" and L (relative angular moment) are related? Does "S-wave" imply that the relative angular moment is 0?

 

[Einj]

Yes, it's just a way of saying it. If you say that a system is in S/D/P-wave you are simply saying that the relative angular momentum of this system is L=0/1/2, nothing more. It's a nomenclature borrowed from atomic physics.

 

[bznm]

Oh, so many thanks! :)

And so, if the prof hadn't said that the pion is captured in S-wave, I wouldn't be able to say that L=0, isn't it?

 

[Einj]

Generally speaking yes. In some cases the relative angular momentum is constrained by total angular momentum and parity conservation.

However, most of the times, a certain process can happen with different L. The distinction between the different cases must be made experimentally.

 

[bznm]

Thanks again!