Understanding Isotropic Decay: Solving Jackson's Problem

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Discussion Overview

The discussion revolves around the concept of 'isotropic decay' as presented in a problem from Jackson's textbook. Participants are exploring the meaning of isotropic decay in the context of particle physics, particularly focusing on its implications in the rest frame of a particle and the Center of Mass frame. The conversation includes attempts to clarify the term and its application to the problem at hand.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on the meaning of 'isotropic decay' in the context of a problem from Jackson's textbook.
  • Another participant defines isotropic as meaning all directions are equally likely.
  • A different participant acknowledges the definition but expresses that it does not aid in solving the problem.
  • One participant proposes that isotropic decay could imply that the magnitudes of spatial momenta and temporal momenta (energy) are almost the same for all decay products.
  • Another participant emphasizes that the term isotropic primarily refers to directions rather than magnitudes.
  • A later reply provides a definition from an instructor, stating that isotropic decay means decay products emerge at all angles with equal probability in the Center of Mass frame, while respecting momentum conservation constraints.

Areas of Agreement / Disagreement

Participants express differing interpretations of isotropic decay, particularly regarding whether it pertains to directions or magnitudes. There is no consensus on the specific meaning as it applies to the problem.

Contextual Notes

Some participants highlight the need for clarity on the definitions and implications of isotropic decay, indicating potential limitations in understanding how it applies to the problem without further context.

dioib
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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.
 
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Isotropic means all directions are equally likely.
 
hamster143 said:
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.
 
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.
 
You are talking about magnitudes. As hamster says, the word refers to directions.
 
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).
 

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