# COM vs Lab Total energy discrepency

1. Oct 26, 2007

### physmurf

I am reading from the book, "Nuclear Reactor Theory", by Lamarsh. I have run across an idea that I am struggling to understand:

It states that for a neutron that scatters elastically with a nucleus, the Energy in the Center of Mass (COM) frame of reference will always be slightly less than the total energy in the lab frame of reference.

For some reason I don't like this. Sure I can follow the mathematics and the explanation, but it doesn't seem right that the total energy would be the same. When I contacted my professor about this, he indicated that this is merely a classical idea. However, for some reason, this just doesn't jive with what I think should be going on.

Anybody have any conceptual explanations on why this is true?

Thanks

2. Oct 26, 2007

### meopemuk

Relativistic energy of any system in any reference frame is given by

$$E = \sqrt{M^2c^4 + \mathbf{P}^2c^2}$$................(1)

where $\mathbf{P}$ is the total momentum and $M$ is the rest mass, which is independent on the reference frame. In the center-of-mass frame the total momentum is zero, so the energy is $E = Mc^2$, which is lower than in any other reference frame (where the total momentum is non-zero).

So, the reason for the excess energy in the lab frame is the fact that the system (neutron + nucleus) has a non-zero momentum.

Eugene.

3. Oct 26, 2007

### Staff: Mentor

...
I guess I don't get what's bugging you. The total energy will always be less in the COM frame.