Parity of a system composed by 2 particles

In summary, the total parity of a system of two particles is given by: P=P_1 P_2 (-1)^L. This means that the parity of the system is the sum of the parities of the particles in the system, minus 1. If you have three particles, you need to first study two of them and obtain the corresponding system. You can then compose this last system with the third particle.
  • #1
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I have read that for a system of 2 particles, the total parity is given by:

[itex]P=P_1 P_2 (-1)^L[/itex] where

- [itex] P_1, P_2[/itex]= insisec parity of particle 1, 2

- L= relative angular moment

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

Many thanks
 
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  • #2
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.
 
  • #3
Einj said:
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 [itex](-1)^L[/itex] =1, but I don't understand why. Could you help me?
 
  • #4
The nomenclature is S-wave (L=0), P-wave (L=1), D-wave (L=2), etc.
 
  • #5
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?
 
  • #6
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.
 
  • #7
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?
 
  • #8
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.
 
  • #9
Thanks again!
 

1. What is the definition of parity in a system composed by 2 particles?

The parity of a system composed by 2 particles is a measure of how the system behaves under the transformation of spatial inversion, where the positions of the particles are reversed. If the system remains unchanged after this transformation, it has a parity of +1 (even parity), and if it changes, it has a parity of -1 (odd parity).

2. How is the parity of a system composed by 2 particles calculated?

The parity of a system composed by 2 particles is calculated by comparing the wave function of the system before and after the spatial inversion transformation. If the wave function remains the same, the parity is +1, and if it changes sign, the parity is -1.

3. What is the significance of parity in a system composed by 2 particles?

The parity of a system composed by 2 particles is significant because it is a fundamental property of the system that affects its behavior and interactions with other particles. It is also used in many physical theories, such as quantum mechanics and particle physics, to describe and predict the behavior of systems.

4. Can the parity of a system composed by 2 particles change?

Yes, the parity of a system composed by 2 particles can change. This can happen when the particles interact with other particles or when they undergo certain transformations. However, in some systems, the parity is conserved, meaning it remains the same regardless of interactions or transformations.

5. How does the parity of a system composed by 2 particles affect its symmetry?

The parity of a system composed by 2 particles is closely related to its symmetry. A system with even parity has a higher degree of symmetry, while a system with odd parity has a lower degree of symmetry. This affects the selection rules for physical processes in the system, as certain symmetries must be conserved during interactions.

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