Understanding Isotropic Decay: Solving Jackson's Problem

[dioib]

I am trying to solve a problem from Jackson's and it says that the decay in particle's rest frame is more or less isotropic. I was wondering if somebody could help me figure the meaning of an 'isotropic decay' here.

Thank you in advance.

 

[hamster143]

Isotropic means all directions are equally likely.

 

[dioib]

Isotropic means all directions are equally likely.

I knew that sense of the term, but that meaning doesn't really help solving the this problem.

 

[dioib]

I think it should mean of the following:
1- the magnitude of spatial momenta is almost the same for all decay products,
2- the magnitude of temporal momenta (energy) is almost the same for all decay products.

But I can't figure out which description is actually meant just from the look of the problem.

 

[Vanadium 50]

You are talking about magnitudes. As hamster says, the word refers to directions.

 

[dioib]

The definition as I heard from the instructor is as follows:

A decay is isotropic if it is so in the Center of Mass frame; in the sense that the decay products come out in all angles with the same probability (but of course with fixed relative angles between them imposed by momentum conservation).