Helicity conservation in scattering

[Josh1079]

Hi,

My question basically comes from this book called "Deep inelastic scattering"

In the second chapter, it first made a similar argument for J = 1 Jz = -1, +1 which is pretty easy to get along with. However, immediately following from that there was this argument which confuses me a bit. I mean if Jz = 0, isn't it also possible to be in the J=1 state |1,0> ? Is there a physical argument for not considering this possibility?

Thanks!

 

[AndyW]

Hello,

Thank you for your question about the book "Deep inelastic scattering". I am familiar with the chapter you mentioned and I can understand your confusion. Let me try to explain it further.

In quantum mechanics, the total angular momentum of a particle can have different values, which are represented by the quantum number J. This value can range from 0 to infinity, with half-integer values for particles with spin. However, for a given value of J, there are different possible orientations of the angular momentum, represented by the quantum number Jz. For example, for J=1, there are three possible orientations: Jz=-1, 0, and +1.

Now, to answer your question, it is indeed possible for Jz to be 0 in the J=1 state. However, in the context of deep inelastic scattering, we are interested in the process of a particle interacting with a target. In this case, the target is usually at rest, which means that the total angular momentum of the system (particle + target) is conserved. This means that the initial and final states must have the same total angular momentum.

In the case of J=1, the possible initial states are Jz=-1, 0, and +1. However, if the target is at rest, the final state must also have Jz=0, as this is the only value that can be conserved. This is why the book only considers the states with Jz=-1 and +1 in this context.

I hope this helps to clarify the reasoning behind not considering the Jz=0 state in this particular case. Please let me know if you have any further questions.