Quantum scattering theory (lab frame, center of mass frame)

[moriheru]

Greetings,
Here is my question:
What is the difference between the labframe and the center of mass frame in QM scattering theory? Is it that in the labframe both particles are moving towards each other and in the center of mass frame one particle is static and a second one is moving towards the stationary particle?
Thanks for any clarifications.

 

[Einj]

The opposite. In the center of mass frame the total momentum of the system vanishes $\vec{P}=\vec{p}_1+\vec{p}_2=0$. In the lab frame one usually takes one of the two momenta to be zero, say $\vec p_2=0$ and hence $\vec P=\vec p_1$.

 

[moriheru]

I see thanks Einji. But why use two frames and not one universal frame, thus translating between frames would be unecessary?

 

[Einj]

Well, first of all there is no such things as a "universal frame". What would it be? Also, usually the center of mass frame is a much easier environment to work out the calculation but most of the experiment are performed with one of the targets fixed and so you want to "translate" your prediction into the lab frame.

 

[moriheru]

Are the frames just different scenarios of scattering?

 

[Nugatory]

Are the frames just different scenarios of scattering?

No. They are the same scenario - the exact same physical interaction - as it would be described by two different observers. It's generally easier to calculate the energies, momenta, and trajectories of the particles using a frame in which the total momentum is zero. Once we have that, we can transform to the lab frame to see what the collision will look like there.

 

[moriheru]

No. They are the same scenario - the exact same physical interaction - as it would be described by two different observers. It's generally easier to calculate the energies, momenta, and trajectories of the particles using a frame in which the total momentum is zero. Once we have that, we can transform to the lab frame to see what the collision will look like there.

Thanks Nugatory,but if the scenarios are the same what is the difference between the threads if they describe the same scenario?

 

[Nugatory]

Thanks Nugatory,but if the scenarios are the same what is the difference?

The ease of calculating the outcome. When you do the calculation in the center of mass frame, you know that the total momentum of the collision products must be zero.

 

[moriheru]

The ease of calculating the outcome. When you do the calculation in the center of mass frame, you know that the total momentum of the collision products must be zero.

So can one use the center of mass frame when the total momentum of the colisionproducts is zero and the labframe when the total momentum of the colisionproducts is nonzero? Thanks Nugatory. Is it due to the conservation of the momentum?

 

[e.bar.goum]

So can one use the center of mass frame when the total momentum of the colisionproducts is zero and the labframe when the total momentum of the colisionproducts is nonzero?

No, you can transform the frame to make the total momentum of the collision products to be zero. For the same reaction, I can describe it in whatever reference frame I like.

I choose the centre of momentum frame to do my calculations in, because it makes them much easier to do, then I may choose to transform to the lab frame when I want to understand what the outcome of the reaction will look like on my detectors.

 

[moriheru]

This thread has helped thanks for all clarifications